Outside Russia very little is known about the terrestrial ecology, vegetation, biogeographical patterns, and biodiversity of the enormously extensive ecosystems of Yakutia, Siberia. These systems are very special in that they function on top of huge layers of permafrost and are exposed to very severe and extreme weather conditions, the range between winter and summer temperatures being more than 100 degrees C. The soils are generally poor, and human use of the vegetation is usually extensive. Main vegetation zones are taiga and tundra, but Yakutia also supports a special land and vegetation form, caused by permafrost, the alas: more or less extensive grasslands around roundish lakes in taiga. All these vegetation types will be described and their ecology and ecophysiological characteristics will be dealt with. Because of the size of Yakutia, covering several climatic zones, and its extreme position on ecological gradients, Yakutia contains very interesting biogeographical patterns, which also will be described. Our analyses are drawn from many years of research in Yakutia and from a vast body of ecological and other literature in Russian publications and in unpublished local reports. The anthropogenic influence on the ecosystems will be dealt with. This includes the main activities of human interference with nature: forestry, extensive reindeer herding, cattle and horse grazing, etc. Also fire and other prominent ecological factors are dealt with. A very important point is also the very high degree of naturalness that is still extant in Yakutia's main vegetation zones.

The book presents the main approaches in study of algebraic structures of symmetries in models of theoretical and mathematical physics, namely groups and Lie algebras and their deformations. It covers the commonly encountered quantum groups (including Yangians). The second main goal of the book is to present a differential geometry of coset spaces that is actively used in investigations of models of quantum field theory, gravity and statistical physics. The third goal is to explain the main ideas about the theory of conformal symmetries, which is the basis of the AdS/CFT correspondence.The theory of groups and symmetries is an important part of theoretical physics. In elementary particle physics, cosmology and related fields, the key role is played by Lie groups and algebras corresponding to continuous symmetries. For example, relativistic physics is based on the Lorentz and Poincare groups, and the modern theory of elementary particles — the Standard Model — is based on gauge (local) symmetry with the gauge group SU(3) x SU(2) x U(1). This book presents constructions and results of a general nature, along with numerous concrete examples that have direct applications in modern theoretical and mathematical physics.

A phenomenon which appears in nature, or human behavior, can sometimes be explained by saying that a certain potential function is maximized, or minimized. For example, the Hamiltonian mechanics, soapy films, size of an atom, business management, etc. In mathematics, a point where a given function attains an extreme value is called a critical point, or a singular point. The purpose of singularity theory is to explore the properties of singular points of functions and mappings.This is a volume on the proceedings of the fourth Japanese-Australian Workshop on Real and Complex Singularities held in Kobe, Japan. It consists of 11 original articles on singularities. Readers will be introduced to some important new notions for characterizations of singularities and several interesting results are delivered. In addition, current approaches to classical topics and state-of-the-art effective computational methods of invariants of singularities are also presented. This volume will be useful not only to the singularity theory specialists but also to general mathematicians.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

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 s (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.

Outside Russia very little is known about the terrestrial ecology, vegetation, biogeographical patterns, and biodiversity of the enormously extensive ecosystems of Yakutia, Siberia. These systems are very special in that they function on top of huge layers of permafrost and are exposed to very severe and extreme weather conditions, the range between winter and summer temperatures being more than 100 degrees C. The soils are generally poor, and human use of the vegetation is usually extensive. Main vegetation zones are taiga and tundra, but Yakutia also supports a special land and vegetation form, caused by permafrost, the alas: more or less extensive grasslands around roundish lakes in taiga. All these vegetation types will be described and their ecology and ecophysiological characteristics will be dealt with. Because of the size of Yakutia, covering several climatic zones, and its extreme position on ecological gradients, Yakutia contains very interesting biogeographical patterns, which also will be described. Our analyses are drawn from many years of research in Yakutia and from a vast body of ecological and other literature in Russian publications and in unpublished local reports. The anthropogenic influence on the ecosystems will be dealt with. This includes the main activities of human interference with nature: forestry, extensive reindeer herding, cattle and horse grazing, etc. Also fire and other prominent ecological factors are dealt with. A very important point is also the very high degree of naturalness that is still extant in Yakutia's main vegetation zones.

In this monograph the author presents a coherent exposition of recent results on complete characterization of Kobayashi-hyperbolic manifolds with high-dimensional groups of holomorphic automorphisms. These classification results can be viewed as complex-geometric analogues of those known for Riemannian manifolds with high-dimensional isotropy groups that were extensively studied in the 1950s-70s.

This book looks at the mathematical foundations of the models currently in use. All existing books on bioinformatics are software-orientated and they concentrate on computer implementations of mathematical models of biology. This book is unique in the sense that it looks at the mathematical foundations of the models, which are crucial for correct interpretation of the outputs of the models.

'Fortresses must carry out the same tasks as the fortresses of old....They must allow themselves to be surrounded and thus tie down as many enemy forces as possible.' So Hitler directed in March 1944 and, in so doing, sealed the fate of Ternopol', Kovel', Poznan and Breslau, cities in the Ukraine and Poland that were in the path of the Red Army's advance towards Nazi Germany. German forces, under orders to resist at all costs, adopted all-round defence and struggled to hold out while waiting for relief - which never came. In this gripping and original book, Alexey Isaev describes, in vivid detail, what happened next -intense and ruthless fighting, horrendous casualties among soldiers and civilians, the fabric of these historic cities torn apart. His account is based on pioneering archival research which offers us an unrivalled insight into the tactics on both sides, the experience of the close-quarter fighting in the streets and houses, and the dreadful aftermath. At the same time he shows why these cities were chosen and how the wider war passed them by as the Wehrmacht retreated and the battlefront moved westward. Each of these cities suffered a similar fate to Stalingrad but their story has never been told before in such graphic and circumstantial detail.

We consider Levi non-degenerate tube hypersurfaces in complex linear space which are "spherical," that is, locally CR-equivalent to the real hyperquadric. Spherical hypersurfaces are characterized by the condition of the vanishing of the CR-curvature form, so such hypersurfaces are flat from the CR-geometric viewpoint. On the other hand, such hypersurfaces are of interest from the point of view of affine geometry. Thus our treatment of spherical tube hypersurfaces in this book is two-fold: CR-geometric and affine-geometric. Spherical tube hypersurfaces turn out to possess remarkable properties. For example, every such hypersurface is real-analytic and extends to a closed real-analytic spherical tube hypersurface in complex space. One of our main goals is to give an explicit affine classification of closed spherical tube hypersurfaces whenever possible. In this book we offer a comprehensive exposition of the theory of spherical tube hypersurfaces starting with the idea proposed in the pioneering work by P. Yang (1982) and ending with the new approach due to G. Fels and W. Kaup (2009).

At its core, this concise textbook presents standard material for a first course in complex analysis at the advanced undergraduate level. This distinctive text will prove most rewarding for students who have a genuine passion for mathematics as well as certain mathematical maturity. Primarily aimed at undergraduates with working knowledge of real analysis and metric spaces, this book can also be used to instruct a graduate course. The text uses a conversational style with topics purposefully apportioned into 21 lectures, providing a suitable format for either independent study or lecture-based teaching. Instructors are invited to rearrange the order of topics according to their own vision. A clear and rigorous exposition is supported by engaging examples and exercises unique to each lecture; a large number of exercises contain useful calculation problems. Hints are given for a selection of the more difficult exercises. This text furnishes the reader with a means of learning complex analysis as well as a subtle introduction to careful mathematical reasoning. To guarantee a student's progression, more advanced topics are spread out over several lectures. This text is based on a one-semester (12 week) undergraduate course in complex analysis that the author has taught at the Australian National University for over twenty years. Most of the principal facts are deduced from Cauchy's Independence of Homotopy Theorem allowing us to obtain a clean derivation of Cauchy's Integral Theorem and Cauchy's Integral Formula. Setting the tone for the entire book, the material begins with a proof of the Fundamental Theorem of Algebra to demonstrate the power of complex numbers and concludes with a proof of another major milestone, the Riemann Mapping Theorem, which is rarely part of a one-semester undergraduate course.

This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ++++ The below data was compiled from various identification fields in the bibliographic record of this title. This data is provided as an additional tool in helping to ensure edition identification: ++++ Socialpolitische Essais Andreĭ Alekseevich Isaev J. H. W. Dietz Nachf., 1902 Social Science; Methodology; Social Science / Methodology; Social Science / Research; Sociology

Substantielles fachliches Wissen ist eine notwendige Grundlage dafur, dass Lehrerinnen und Lehrer einen attraktiven und erfolgreichen Mathematikunterricht gestalten koennen. Wie aber muss dieses fachliche Wissen genau aussehen? Auf welche Weise wird es bei der Planung und Durchfuhrung von Unterricht genutzt? Wie kann man es im Studium auf eine Weise erwerben, die es fur didaktisches Handeln anschlussfahig macht? Der vorliegende Band gibt Antworten auf diese Fragen. Er diskutiert koharenzstiftende Lerngelegenheiten in der Lehramtsausbildung, die in regularen Veranstaltungen an Hochschulen systematisch evaluiert wurden.Im ersten Teil des Bandes steht die Professionsorientierung in Vorlesungen zum Lehramtsstudium im Fokus. Dabei wird der Frage nachgegangen, wie das mathematische Fachwissen einer Lehrkraft beschaffen sein muss, um unterrichtlich wirksam zu werden. Auf der Basis verschiedener theoretischer Modelle werden dazu mathematische Grundveranstaltungen im Lehramtsstudium analysiert. Im zweiten Teil des Bandes stehen UEbungsveranstaltungen mit einem Schwerpunkt auf der Gestaltung von Aufgaben im Mittelpunkt. Neben einer Klassifikation von Aufgaben werden Konzepte vorgestellt, wie durch spezifische UEbungen der Zusammenhang zwischen Hochschulmathematik und der professionellen Tatigkeit von Lehrkraften deutlich gemacht werden kann. Im dritten Teil des Bandes werden schliesslich Seminare als weitere Form der professionsorientierten Ausbildung von Lehrkraften betrachtet. Hierbei geht es um spezifische Aspekte der Professionsorientierung wie etwa die Kompetenz zur Nutzung digitaler Werkzeuge oder vertiefende mathematische Themen wie die Differentialgeometrie. Die Evaluationen in den drei Veranstaltungsformen zielen auf die Bewertung von Materialien, die kognitive Entwicklung und schliesslich die Veranderung von affektiven Variablen der Lehramtsstudierenden.

In der folgenden Arbeit wird eine wissenschaftliche Untersuchung der aktuellen russischen Standards unternommen. Die IAS/IFRS sollen dazu eine Hilfestellung leisten und nicht n her untersucht werden. Die wissenschaftliche Untersuchung der konzeptionellen Rechnungslegungsgrundlagen der Buchf hrung in der Markwirtschaft Russlands sowie der Ansatz und die Bewertung ausgew hlter Bilanzpositionen des handelsrechtlichen Einzeljahresabschlusses gew hren einen Einblick in die handelsrechtliche Rechnungslegung in der Russischen F deration. In der vorliegenden Arbeit wird zudem der Geltungsbereich der handelsrechtlichen Rechnungslegung dargestellt. Auf die Bestandteile des handelsrechtlichen Jahresabschlusses kann aus Platzgr nden und zur Vermeidung einer oberfl chlichen Betrachtung nicht eingegangen werden. In den russischen Rechnungslegungsstandards existieren dar ber hinaus in der Gesetzgebung nicht explizit behandelte F lle. In dieser Arbeit werden ausschlie lich die geregelten F lle beschrieben, auf die Handhabung von "L cken" und Spezialf llen kann nicht n her eingegangen werden.