Download or read book Finiteness Conditions and Generalized Soluble Groups written by Derek J.S. Robinson and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a study of group theoretical properties of two disparate kinds, firstly finiteness conditions or generalizations of finiteness and secondly generalizations of solubility or nilpotence. It will be particularly interesting to discuss groups which possess properties of both types. The origins of the subject may be traced back to the nineteen twenties and thirties and are associated with the names of R. Baer, S.N. Cernikov, K.A. Hirsch, A.G. Kuros, 0.]. Schmidt and H. Wielandt. Since this early period, the body of theory has expanded at an increasingly rapid rate through the efforts of many group theorists, particularly in Germany, Great Britain and the Soviet Union. Some of the highest points attained can, perhaps, be found in the work of P. Hall and A.I. Mal'cev on infinite soluble groups. Kuras's well-known book "The theory of groups" has exercised a strong influence on the development of the theory of infinite groups: this is particularly true of the second edition in its English translation of 1955. To cope with the enormous increase in knowledge since that date, a third volume, containing a survey of the contents of a very large number of papers but without proofs, was added to the book in 1967

Download or read book Generalized Neutrosophic Extended Triplet Group written by Yingcang Ma and published by Infinite Study. This book was released on with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neutrosophic extended triplet group is a new algebra structure and is different from the classical group. In this paper, the notion of generalized neutrosophic extended triplet group is proposed and some properties are discussed.

Download or read book Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups written by Drew Armstrong and published by American Mathematical Soc.. This book was released on 2009-10-08 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir is a refinement of the author's PhD thesis -- written at Cornell University (2006). It is primarily a desription of new research but also includes a substantial amount of background material. At the heart of the memoir the author introduces and studies a poset $NC^{(k)}(W)$ for each finite Coxeter group $W$ and each positive integer $k$. When $k=1$, his definition coincides with the generalized noncrossing partitions introduced by Brady and Watt in $K(\pi, 1)$'s for Artin groups of finite type and Bessis in The dual braid monoid. When $W$ is the symmetric group, the author obtains the poset of classical $k$-divisible noncrossing partitions, first studied by Edelman in Chain enumeration and non-crossing partitions.

Download or read book Geometric Theory of Generalized Functions with Applications to General Relativity written by M. Grosser and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past few years a certain shift of focus within the theory of algebras of generalized functions (in the sense of J. F. Colombeau) has taken place. Originating in infinite dimensional analysis and initially applied mainly to problems in nonlinear partial differential equations involving singularities, the theory has undergone a change both in in ternal structure and scope of applicability, due to a growing number of applications to questions of a more geometric nature. The present book is intended to provide an in-depth presentation of these develop ments comprising its structural aspects within the theory of generalized functions as well as a (selective but, as we hope, representative) set of applications. This main purpose of the book is accompanied by a number of sub ordinate goals which we were aiming at when arranging the material included here. First, despite the fact that by now several excellent mono graphs on Colombeau algebras are available, we have decided to give a self-contained introduction to the field in Chapter 1. Our motivation for this decision derives from two main features of our approach. On the one hand, in contrast to other treatments of the subject we base our intro duction to the field on the so-called special variant of the algebras, which makes many of the fundamental ideas of the field particularly transpar ent and at the same time facilitates and motivates the introduction of the more involved concepts treated later in the chapter.

Download or read book Generalized Polygons written by Hendrik Van Maldeghem and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Polygons is the first book to cover, in a coherent manner, the theory of polygons from scratch. In particular, it fills elementary gaps in the literature and gives an up-to-date account of current research in this area, including most proofs, which are often unified and streamlined in comparison to the versions generally known. Generalized Polygons will be welcomed both by the student seeking an introduction to the subject as well as the researcher who will value the work as a reference. In particular, it will be of great value for specialists working in the field of generalized polygons (which are, incidentally, the rank 2 Tits-buildings) or in fields directly related to Tits-buildings, incidence geometry and finite geometry. The approach taken in the book is of geometric nature, but algebraic results are included and proven (in a geometric way!). A noteworthy feature is that the book unifies and generalizes notions, definitions and results that exist for quadrangles, hexagons, octagons - in the literature very often considered separately - to polygons. Many alternative viewpoints given in the book heighten the sense of beauty of the subject and help to provide further insight into the matter.​

Download or read book Bituminous Coal Fields of Pennsylvania written by Geological Survey of Pennsylvania and published by . This book was released on 1928 with total page 1240 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Symmetry in Finite Generalized Quadrangles written by Koen Thas and published by Springer Science & Business Media. This book was released on 2004-01-26 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph classifies finite generalized quadrangles by symmetry, generalizing the celebrated Lenz-Barlotti classification for projective planes. The book introduces combinatorial, geometrical and group-theoretical concepts that arise in the classification and in the general theory of finite generalized quadrangles, including automorphism groups, elation and translation generalized quadrangles, generalized ovals and generalized ovoids, span-symmetric generalized quadrangles, flock geometry and property (G), regularity and nets, split BN-pairs of rank 1, and the Moufang property.

Download or read book Finite Generalized Quadrangles written by Stanley E. Payne and published by European Mathematical Society. This book was released on 2009 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized quadrangles (GQ) were formally introduced by J. Tits in 1959 to describe geometric properties of simple groups of Lie type of rank 2. The first edition of Finite Generalized Quadrangles (FGQ) quickly became the standard reference for finite GQ. The second edition is essentially a reprint of the first edition. It is a careful rendering into LaTeX of the original, along with an appendix that brings to the attention of the reader those major new results pertaining to GQ, especially in those areas where the authors of this work have made a contribution. The first edition has been out of print for many years. The new edition makes available again this classical reference in the rapidly increasing field of finite geometries.

Download or read book Some Generalized Probability Distributions with Special Reference to the Mineral Industries written by Robert M. Becker and published by . This book was released on 1964 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Character Map In Non abelian Cohomology The Twisted Differential And Generalized written by Domenico Fiorenza and published by World Scientific. This book was released on 2023-08-11 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a novel development of fundamental and fascinating aspects of algebraic topology and mathematical physics: 'extra-ordinary' and further generalized cohomology theories enhanced to 'twisted' and differential-geometric form, with focus on, firstly, their rational approximation by generalized Chern character maps, and then, the resulting charge quantization laws in higher n-form gauge field theories appearing in string theory and the classification of topological quantum materials.Although crucial for understanding famously elusive effects in strongly interacting physics, the relevant higher non-abelian cohomology theory ('higher gerbes') has had an esoteric reputation and remains underdeveloped.Devoted to this end, this book's theme is that various generalized cohomology theories are best viewed through their classifying spaces (or moduli stacks) — not necessarily infinite-loop spaces — from which perspective the character map is really an incarnation of the fundamental theorem of rational homotopy theory, thereby not only uniformly subsuming the classical Chern character and a multitude of scattered variants that have been proposed, but now seamlessly applicable in the hitherto elusive generality of (twisted, differential, and) non-abelian cohomology.In laying out this result with plenty of examples, this book provides a modernized introduction and review of fundamental classical topics: 1. abstract homotopy theory via model categories; 2. generalized cohomology in its homotopical incarnation; 3. rational homotopy theory seen via homotopy Lie theory, whose fundamental theorem we recast as a (twisted) non-abelian de Rham theorem, which naturally induces the (twisted) non-abelian character map.

Download or read book Some Generalized Kac Moody Algebras with Known Root Multiplicities written by Peter Niemann and published by American Mathematical Soc.. This book was released on 2002 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from Borcherds' fake monster Lie algebra, this text construct a sequence of six generalized Kac-Moody algebras whose denominator formulas, root systems and all root multiplicities can be described explicitly. The root systems decompose space into convex holes, of finite and affine type, similar to the situation in the case of the Leech lattice. As a corollary, we obtain strong upper bounds for the root multiplicities of a number of hyperbolic Lie algebras, including $AE_3$.

Download or read book Generalized Seizures From Clinical Phenomenology to Underlying Systems and Networks written by Edouard HIRSCH and published by John Libbey Eurotext. This book was released on 2006-01-01 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book is the fruit of a workshop, designed as a discussion forum, with the participation of experts from all over the world, to extensively review clinical, neurophysiological and fundamental research available data in order to generate new axes for research, clinical practice and care. The first section traces back to the definitions and concepts underlying the terms “generalized seizures and epilepsies”. Section II reviews human and animal data suggesting that the brainstem network plays an important role for tonic seizures generation. The third and fourth sections analyze recent knowledge on cortico-thalamic and basal ganglia networks in absence and myoclonic seizures, both in animal models and in humans. The fifth section compares the phenomenology of “Primary versus Secondary Tonico-clonic seizures”, including animal data, clinical expression in humans and genetics. Section VI goes back to the discussion “Cortical” versus “Centrencephalic” theories. The last two chapters thoroughly review the clinical applications of current knowledge, in terms of pharmacological approach and clinical care.

Download or read book Generalized Ricci Flow written by Mario Garcia-Fernandez and published by American Mathematical Soc.. This book was released on 2021-04-06 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: The generalized Ricci flow is a geometric evolution equation which has recently emerged from investigations into mathematical physics, Hitchin's generalized geometry program, and complex geometry. This book gives an introduction to this new area, discusses recent developments, and formulates open questions and conjectures for future study. The text begins with an introduction to fundamental aspects of generalized Riemannian, complex, and Kähler geometry. This leads to an extension of the classical Einstein-Hilbert action, which yields natural extensions of Einstein and Calabi-Yau structures as ‘canonical metrics’ in generalized Riemannian and complex geometry. The book then introduces generalized Ricci flow as a tool for constructing such metrics and proves extensions of the fundamental Hamilton/Perelman regularity theory of Ricci flow. These results are refined in the setting of generalized complex geometry, where the generalized Ricci flow is shown to preserve various integrability conditions, taking the form of pluriclosed flow and generalized Kähler-Ricci flow, leading to global convergence results and applications to complex geometry. Finally, the book gives a purely mathematical introduction to the physical idea of T-duality and discusses its relationship to generalized Ricci flow. The book is suitable for graduate students and researchers with a background in Riemannian and complex geometry who are interested in the theory of geometric evolution equations.

Download or read book Generalized Epilepsy written by AVOLI and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there has been intense interest in the basic mechanisms of epilepsy. Many symposia and monographs have been devoted to this topic. These reviews, however, have focused almost exclusively on studies performed in models of partial (or focal) epilepsy. It was natural that scientists interested in the fundamental mechanism of epileptogenesis at the cellular level were attracted to work on models in which the epileptogenic dysfunction could be confined to ever-smaller populations of neurons. Many of the most illuminating studies done in this field in the recent past have been carried out in vitro on brain slices or on dissociated neuronal cultures. Much valuable insight into the mechanisms of epileptogenesis has been obtained in this manner. One cannot, however, automatically assume that mechanisms elucidated in such exquisitely "focal" models are applicable to forms of epilepsy in which seizures from their very start involve the entire brain. One of the most difficult questions that arises in this context is how epileptogenic dysfunction, which can be understood in terms of mechanisms involving a few contiguous cells, can lead to what appears to be a simultaneous onset of seizure discharge in virtually all areas of the brain. Most of the workers who have made excellent contributions to the understanding of the cellular mechanisms involved in epileptogenesis have paid virtually no attention to this important problem.

Download or read book Finiteness Conditions and Generalized Soluble Groups written by Derek J.S. Robinson and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a study of group theoretical properties of two dis parate kinds, firstly finiteness conditions or generalizations of fini teness and secondly generalizations of solubility or nilpotence. It will be particularly interesting to discuss groups which possess properties of both types. The origins of the subject may be traced back to the nineteen twenties and thirties and are associated with the names of R. Baer, S. N. Cernikov, K. A. Hirsch, A. G. Kuros, 0.]. Schmidt and H. Wie landt. Since this early period, the body of theory has expanded at an increasingly rapid rate through the efforts of many group theorists, particularly in Germany, Great Britain and the Soviet Union. Some of the highest points attained can, perhaps, be found in the work of P. Hall and A. I. Mal'cev on infinite soluble groups. Kuras's well-known book "The theory of groups" has exercised a strong influence on the development of the theory of infinite groups: this is particularly true of the second edition in its English translation of 1955. To cope with the enormous increase in knowledge since that date, a third volume, containing a survey of the contents of a very large number of papers but without proofs, was added to the book in 1967.

Download or read book Nonlinear Theory of Generalized Functions written by Michael Oberguggenberger and published by CRC Press. This book was released on 1999-03-16 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Questions regarding the interplay of nonlinearity and the creation and propagation of singularities arise in a variety of fields-including nonlinear partial differential equations, noise-driven stochastic partial differential equations, general relativity, and geometry with singularities. A workshop held at the Erwin-Schrödinger International Institute for Mathematical Physics in Vienna investigated these questions and culminated in this volume of invited papers from experts in the fields of nonlinear partial differential equations, structure theory of generalized functions, geometry and general relativity, stochastic partial differential equations, and nonstandard analysis. The authors provide the latest research relevant to work in partial differential equations, mathematical physics, and nonlinear analysis. With a focus on applications, this books provides a compilation of recent approaches to the problem of singularities in nonlinear models. The theory of differential algebras of generalized functions serves as the central theme of the project, along with its interrelations with classical methods.

Download or read book Conformal Blocks Generalized Theta Functions and the Verlinde Formula written by Shrawan Kumar and published by Cambridge University Press. This book was released on 2021-11-25 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1988, E. Verlinde gave a remarkable conjectural formula for the dimension of conformal blocks over a smooth curve in terms of representations of affine Lie algebras. Verlinde's formula arose from physical considerations, but it attracted further attention from mathematicians when it was realized that the space of conformal blocks admits an interpretation as the space of generalized theta functions. A proof followed through the work of many mathematicians in the 1990s. This book gives an authoritative treatment of all aspects of this theory. It presents a complete proof of the Verlinde formula and full details of the connection with generalized theta functions, including the construction of the relevant moduli spaces and stacks of G-bundles. Featuring numerous exercises of varying difficulty, guides to the wider literature and short appendices on essential concepts, it will be of interest to senior graduate students and researchers in geometry, representation theory and theoretical physics.