Boris Khesin

Dannaja kniga - eto pervaja monografija, v kotoroj topologicheskie, teoretiko-gruppovye i geometricheskie zadachi idealnoj gidrodinamiki i magnitogidrodinamiki rassmatrivajutsja s edinoj tochki zrenija. Neobkhodimyj podgotovitelnyj material iz gidrodinamiki i chistoj matematiki izlagaetsja s bolshim kolichestvom primerov i risunkov. Kniga prednaznachena dlja studentov, aspirantov i spetsialistov po chistoj ili prikladnoj matematike, rabotajuschikh v takikh oblastjakh, kak gidrodinamika, gruppy Li, dinamicheskie sistemy i differentsialnaja geometrija. Predyduschee izdanie knigi vyshlo v 2007 g. Nastojaschee izdanie dopolneno spetsialno podgotovlennym obzorom poslednikh dostizhenij topologicheskoj gidrodinamiki.2-e izdanie, dopolnennoe.

The subject of this book is the methodology and results of integrated geophysical investigations in the Caucasian region, mainly interpretation of magnetic and gravity anomalies with utilization of a huge petrophysical database for the evaluation of geological structure and mineral resources. Relative voluminous geophysical data are useful for the Earth Sciences researchers interested in the Caucasian region (and adjacent and similar regions) characterized by complicated geological structure, inclined magnetization (polarization), uneven topography and mountain/sea transition. Examination of geophysical fields verified by super-deep wells drilling indicates that magmatic rocks of the Lesser Caucasus are extended northward under thick sedimentary cover of the Kura Depression up to the Greater Caucasus. These rocks form hidden petroleum-bearing traps of a newly identified type. On the basis of geophysical studies (mainly inexpensive magnetic and electric methods), a new copper-polymetallic province in the Greater Caucasus has been revealed. a newly developed integrated approach and special information-statistical techniques for processing and interpretation of geophysical data facilitate detection of important geological features, e.g. hidden intersections of linear structures that control location of large commercial ore and oil-and-gas deposits, as well as focuses of dangerous geodynamic events at a depth. Numerous illustrations (including colour) elucidate different problems and solutions on various scales and in diverse geological-geophysical environments. Many aspects of this book have been presented at the teaching courses for bachelors, masters and doctors at the Tel-Aviv University (Tel Aviv, Israel) and Ben-Gurion University (Be’er-Sheva, Israel). Benefits to readers are predetermined by the combination of the authors many-years personal experience in the geophysical studies of Azerbaijan and other regions of the Caucasus with the authors' knowledgeof the modern level of geophysics in the world.

The subject of this book is the methodology and results of integrated geophysical investigations in the Caucasian region, mainly interpretation of magnetic and gravity anomalies with utilization of a huge petrophysical database for the evaluation of geological structure and mineral resources. Relative voluminous geophysical data are useful for the Earth Sciences researchers interested in the Caucasian region (and adjacent and similar regions) characterized by complicated geological structure, inclined magnetization (polarization), uneven topography and mountain/sea transition. Examination of geophysical fields verified by super-deep wells drilling indicates that magmatic rocks of the Lesser Caucasus are extended northward under thick sedimentary cover of the Kura Depression up to the Greater Caucasus. These rocks form hidden petroleum-bearing traps of a newly identified type. On the basis of geophysical studies (mainly inexpensive magnetic and electric methods), a new copper-polymetallic province in the Greater Caucasus has been revealed. a newly developed integrated approach and special information-statistical techniques for processing and interpretation of geophysical data facilitate detection of important geological features, e.g. hidden intersections of linear structures that control location of large commercial ore and oil-and-gas deposits, as well as focuses of dangerous geodynamic events at a depth. Numerous illustrations (including colour) elucidate different problems and solutions on various scales and in diverse geological-geophysical environments. Many aspects of this book have been presented at the teaching courses for bachelors, masters and doctors at the Tel-Aviv University (Tel Aviv, Israel) and Ben-Gurion University (Be’er-Sheva, Israel). Benefits to readers are predetermined by the combination of the authors many-years personal experience in the geophysical studies of Azerbaijan and other regions of the Caucasus with the authors' knowledgeof the modern level of geophysics in the world.

Helmholtz's seminal paper on vortex motion (1858) marks the beginning of what is now called topological fluid mechanics. After 150 years of work, the field has grown considerably. In the last several decades unexpected developments have given topological fluid mechanics new impetus, benefiting from the impressive progress in knot theory and geometric topology on the one hand, and in mathematical and computational fluid dynamics on the other. This volume contains a wide-ranging collection of up-to-date, valuable research papers written by some of the most eminent experts in the field. Topics range from fundamental aspects of mathematical fluid mechanics, including topological vortex dynamics and magnetohydrodynamics, integrability issues, Hamiltonian structures and singularity formation, to DNA tangles and knotted DNAs in sedimentation. A substantial introductory chapter on knots and links, covering elements of modern braid theory and knot polynomials, as well as more advanced topics in knot classification, provides an invaluable addition to this material.

The aim of this monograph is to give an overview of various classes of in?ni- dimensional Lie groups and their applications, mostly in Hamiltonian - chanics, ?uid dynamics, integrable systems, and complex geometry. We have chosen to present the unifying ideas of the theory by concentrating on speci?c typesandexamplesofin?nite-dimensionalLiegroups. Ofcourse,theselection of the topics is largely in?uenced by the taste of the authors, but we hope thatthisselectioniswideenoughtodescribevariousphenomenaarisinginthe geometry of in?nite-dimensional Lie groups and to convince the reader that they are appealing objects to study from both purely mathematical and more applied points of view. This book can be thought of as complementary to the existing more algebraic treatments, in particular, those covering the str- ture and representation theory of in?nite-dimensional Lie algebras, as well as to more analytic ones developing calculus on in?nite-dimensional manifolds. This monograph originated from advanced graduate courses and mi- courses on in?nite-dimensional groups and gauge theory given by the ?rst author at the University of Toronto, at the CIRM in Marseille, and at the Ecole Polytechnique in Paris in 2001-2004. It is based on various classical and recentresultsthathaveshapedthisnewlyemergedpartofin?nite-dimensional geometry and group theory. Our intention was to make the book concise, relatively self-contained, and useful in a graduate course. For this reason, throughout the text, we have included a large number of problems, ranging from simple exercises to open questions.

The aim of this monograph is to give an overview of various classes of in?ni- dimensional Lie groups and their applications, mostly in Hamiltonian - chanics, ?uid dynamics, integrable systems, and complex geometry. We have chosen to present the unifying ideas of the theory by concentrating on speci?c typesandexamplesofin?nite-dimensionalLiegroups. Ofcourse,theselection of the topics is largely in?uenced by the taste of the authors, but we hope thatthisselectioniswideenoughtodescribevariousphenomenaarisinginthe geometry of in?nite-dimensional Lie groups and to convince the reader that they are appealing objects to study from both purely mathematical and more applied points of view. This book can be thought of as complementary to the existing more algebraic treatments, in particular, those covering the str- ture and representation theory of in?nite-dimensional Lie algebras, as well as to more analytic ones developing calculus on in?nite-dimensional manifolds. This monograph originated from advanced graduate courses and mi- courses on in?nite-dimensional groups and gauge theory given by the ?rst author at the University of Toronto, at the CIRM in Marseille, and at the Ecole Polytechnique in Paris in 2001-2004. It is based on various classical and recentresultsthathaveshapedthisnewlyemergedpartofin?nite-dimensional geometry and group theory. Our intention was to make the book concise, relatively self-contained, and useful in a graduate course. For this reason, throughout the text, we have included a large number of problems, ranging from simple exercises to open questions.