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Lie Symmetry Analysis of Fractional Differential Equations

Lie Symmetry Analysis of Fractional Differential Equations

Mir Sajjad Hashemi; Dumitru Baleanu

CRC Press
2020
sidottu
The trajectory of fractional calculus has undergone several periods of intensive development, both in pure and applied sciences. During the last few decades fractional calculus has also been associated with the power law effects and its various applications. It is a natural to ask if fractional calculus, as a nonlocal calculus, can produce new results within the well-established field of Lie symmetries and their applications. In Lie Symmetry Analysis of Fractional Differential Equations the authors try to answer this vital question by analyzing different aspects of fractional Lie symmetries and related conservation laws. Finding the exact solutions of a given fractional partial differential equation is not an easy task, but is one that the authors seek to grapple with here. The book also includes generalization of Lie symmetries for fractional integro differential equations. Features Provides a solid basis for understanding fractional calculus, before going on to explore in detail Lie Symmetries and their applications Useful for PhD and postdoc graduates, as well as for all mathematicians and applied researchers who use the powerful concept of Lie symmetries Filled with various examples to aid understanding of the topics
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Lie Symmetry Analysis of Fractional Differential Equations

Lie Symmetry Analysis of Fractional Differential Equations

Mir Sajjad Hashemi; Dumitru Baleanu

TAYLOR FRANCIS LTD
2022
nidottu
The trajectory of fractional calculus has undergone several periods of intensive development, both in pure and applied sciences. During the last few decades fractional calculus has also been associated with the power law effects and its various applications. It is a natural to ask if fractional calculus, as a nonlocal calculus, can produce new results within the well-established field of Lie symmetries and their applications. In Lie Symmetry Analysis of Fractional Differential Equations the authors try to answer this vital question by analyzing different aspects of fractional Lie symmetries and related conservation laws. Finding the exact solutions of a given fractional partial differential equation is not an easy task, but is one that the authors seek to grapple with here. The book also includes generalization of Lie symmetries for fractional integro differential equations. Features Provides a solid basis for understanding fractional calculus, before going on to explore in detail Lie Symmetries and their applications Useful for PhD and postdoc graduates, as well as for all mathematicians and applied researchers who use the powerful concept of Lie symmetries Filled with various examples to aid understanding of the topics
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Lie Detection and the Law

Lie Detection and the Law

Andrew Balmer

Routledge
2019
nidottu
This book develops a sociological account of lie detection practices and uses this to think about lying more generally. Bringing together insights from sociology, social history, socio-legal studies and science and technology studies (STS), it explores how torture and technology have been used to try to discern the truth. It examines a variety of socio-legal practices, including trial by ordeal in Europe, the American criminal jury trial, police interrogations using the polygraph machine, and the post-conviction management of sex offenders in the USA and the UK. Moving across these different contexts, it articulates how uncertainties in the use of lie detection technologies are managed, and the complex roles they play in legal spaces. Alongside this story, the book surveys some of the different ways in which lying is understood in philosophy, law and social order. Lie Detection and the Law will be of interest to STS researchers, socio-legal scholars, criminologists and sociologists, as well as others working at the intersections of law and science.
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Lie Groups

Lie Groups

Claudio Procesi

Springer-Verlag New York Inc.
2006
nidottu
Lie groups has been an increasing area of focus and rich research since the middle of the 20th century. Procesi's masterful approach to Lie groups through invariants and representations gives the reader a comprehensive treatment of the classical groups along with an extensive introduction to a wide range of topics associated with Lie groups: symmetric functions, theory of algebraic forms, Lie algebras, tensor algebra and symmetry, semisimple Lie algebras, algebraic groups, group representations, invariants, Hilbert theory, and binary forms with fields ranging from pure algebra to functional analysis. Key to this unique exposition is the large amount of background material presented so the book is accessible to a reader with relatively modest mathematical background. Historical information, examples, exercises are all woven into the text. Lie Groups: An Approach through Invariants and Representations will engage a broad audience, including advanced undergraduates, graduates, mathematicians in a variety of areas from pure algebra to functional analysis and mathematical physics.
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Lie Sphere Geometry

Lie Sphere Geometry

Thomas E. Cecil

Springer-Verlag New York Inc.
2007
nidottu
Thomas Cecil is a math professor with an unrivalled grasp of Lie Sphere Geometry. Here, he provides a clear and comprehensive modern treatment of the subject, as well as its applications to the study of Euclidean submanifolds. It begins with the construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres, and Lie sphere transformations. This new edition contains revised sections on taut submanifolds, compact proper Dupin submanifolds, reducible Dupin submanifolds, and the cyclides of Dupin. Completely new material on isoparametric hypersurfaces in spheres and Dupin hypersurfaces with three and four principal curvatures is also included. The author surveys the known results in these fields and indicates directions for further research and wider application of the methods of Lie sphere geometry.
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Lie Groups, Lie Algebras, and Their Representations

Lie Groups, Lie Algebras, and Their Representations

V.S. Varadarajan

Springer-Verlag New York Inc.
1984
sidottu
This book has grown out of a set of lecture notes I had prepared for a course on Lie groups in 1966. When I lectured again on the subject in 1972, I revised the notes substantially. It is the revised version that is now appearing in book form. The theory of Lie groups plays a fundamental role in many areas of mathematics. There are a number of books on the subject currently available -most notably those of Chevalley, Jacobson, and Bourbaki-which present various aspects of the theory in great depth. However, 1 feei there is a need for a single book in English which develops both the algebraic and analytic aspects of the theory and which goes into the representation theory of semi­ simple Lie groups and Lie algebras in detail. This book is an attempt to fiii this need. It is my hope that this book will introduce the aspiring graduate student as well as the nonspecialist mathematician to the fundamental themes of the subject. I have made no attempt to discuss infinite-dimensional representations. This is a very active field, and a proper treatment of it would require another volume (if not more) of this size. However, the reader who wants to take up this theory will find that this book prepares him reasonably well for that task.
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Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics

Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics

D. H. Sattinger; O. L. Weaver

Springer-Verlag New York Inc.
1986
sidottu
This book is intended as an introductory text on the subject of Lie groups and algebras and their role in various fields of mathematics and physics. It is written by and for researchers who are primarily analysts or physicists, not algebraists or geometers. Not that we have eschewed the algebraic and geo­ metric developments. But we wanted to present them in a concrete way and to show how the subject interacted with physics, geometry, and mechanics. These interactions are, of course, manifold; we have discussed many of them here-in particular, Riemannian geometry, elementary particle physics, sym­ metries of differential equations, completely integrable Hamiltonian systems, and spontaneous symmetry breaking. Much ofthe material we have treated is standard and widely available; but we have tried to steer a course between the descriptive approach such as found in Gilmore and Wybourne, and the abstract mathematical approach of Helgason or Jacobson. Gilmore and Wybourne address themselvesto the physics community whereas Helgason and Jacobson address themselves to the mathematical community. This book is an attempt to synthesize the two points of view and address both audiences simultaneously. We wanted to present the subject in a way which is at once intuitive, geometric, applications­ oriented, mathematically rigorous, and accessible to students and researchers without an extensive background in physics, algebra, or geometry.
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Lie After Lie: The True Story of A Master of Deception, Betrayal, and Murder

Lie After Lie: The True Story of A Master of Deception, Betrayal, and Murder

Lara Bricker

BERKLEY BOOKS
2010
pokkari
A seemingly perfect world held an even more unlikely killer... Julie Keown had a great job, financial security, and a perfect husband who was attending Harvard Business School. But after Julie suddenly died, and doctors discovered she's been poisoned with the main ingredient in antifreeze, her parents began to suspect that her husband, James, was not so perfect. This blow-by-blow account shows how investigators and state police unraveled James Keown's chilling web of deceit.
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Lie to Me

Lie to Me

Tori St. Claire

Penguin USA
2012
pokkari
After helping to break up a Russian human trafficking ring as part of the CIA’s elite Black Opal team, Alexei Nikanova’s newest assignment is to rescue one of the stolen women and return her to her father. When he arrives in Dubai, he discovers his target is Sasha Zablosky—a woman he knows all too well, and who has haunted him ever since their one unforgettable night together. But he finds Sasha reluctant to leave her Sheik, the only true friend she’s ever known. Only Alexei can’t give her a choice. With their yearning roused by intrigue, Alexei and Sasha can no longer resist and spend night after night in forbidden pleasure. Soon Alexei finds himself falling for her even as he battles a shadowy menace to protect her. But Sasha is no innocent. She has a past darker than she could ever admit or that Alexei could ever forgive. And it is about to explode into her life once more. Now, as the lies they tell themselves—and each other—pull them deeper into a perilous desire, what began as simple passion becomes a love certain to destroy them and end the lives of countless innocents.
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Lie Algebras: Theory and Algorithms

Lie Algebras: Theory and Algorithms

W.A. de Graaf

North-Holland
2000
sidottu
The aim of the present work is two-fold. Firstly it aims at a giving an account of many existing algorithms for calculating with finite-dimensional Lie algebras. Secondly, the book provides an introduction into the theory of finite-dimensional Lie algebras. These two subject areas are intimately related. First of all, the algorithmic perspective often invites a different approach to the theoretical material than the one taken in various other monographs (e.g., [42], [48], [77], [86]). Indeed, on various occasions the knowledge of certain algorithms allows us to obtain a straightforward proof of theoretical results (we mention the proof of the Poincaré-Birkhoff-Witt theorem and the proof of Iwasawa's theorem as examples). Also proofs that contain algorithmic constructions are explicitly formulated as algorithms (an example is the isomorphism theorem for semisimple Lie algebras that constructs an isomorphism in case it exists). Secondly, the algorithms can be used to arrive at a better understanding of the theory. Performing the algorithms in concrete examples, calculating with the concepts involved, really brings the theory of life.
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Lie Down with Lions

Lie Down with Lions

Ken Follett

PENGUIN BOOKS
2003
nidottu
"Vintage Follett . . . This is his most ambitious novel and it succeeds admirably." --USA Today Ellis, the American. Jean-Pierre, the Frenchman. They were two men on opposite sides of the Cold War, with a woman torn between them. Together, they formed a triangle of passion and deception, racing from terrorist bombs in Paris to the violence and intrigue of Afghanistan--to the moment of truth and deadly decision for all of them. . . .
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Lie Algebras with Triangular Decompositions

Lie Algebras with Triangular Decompositions

Robert V. Moody; Arturo Pianzola

John Wiley Sons Inc
1995
sidottu
Imparts a self-contained development of the algebraic theory of Kac-Moody algebras, their representations and close relatives--the Virasoro and Heisenberg algebras. Focuses on developing the theory of triangular decompositions and part of the Kac-Moody theory not specific to the affine case. Also covers lattices, and finite root systems, infinite-dimensional theory, Weyl groups and conjugacy theorems.
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Lie Groups, Lie Algebras & Some of Their Applications

Lie Groups, Lie Algebras & Some of Their Applications

Robert Gilmore

Dover Publications Inc.
2006
nidottu
This text introduces graduate students to Lie group theory and its physical applications with rigor and clarity. An opening discussion of introductory concepts leads to explorations of the classical groups, continuous groups and Lie groups, and Lie groups and Lie algebras. Some simple but illuminating examples are followed by examinations of classical algebras, Lie algebras and root spaces, root spaces and Dynkin diagrams, real forms, and contractions and expansions. Reinforced by numerous exercises, solved problems, and figures, the text concludes with a bibliography and indexes. 1974 ed. 75 figures. 17 tables.
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Lie Group

Lie Group

P. M. Cohn

Cambridge University Press
2009
pokkari
The theory of Lie groups rests on three pillars: analysis, topology and algebra. Correspondingly it is possible to distinguish several phases, overlapping in some degree, in its development. It also allows one to regard the subject from different points of view, and it is the algebraic standpoint which has been chosen in this tract as the most suitable one for a first introduction to the subject. The aim has been to develop the beginnings of the theory of Lie groups, especially the fundamental theorems of Lie relating the group to its infinitesimal generators (the Lie algebra); this account occupies the first five chapters. Next to Lie's theorems in importance come the basic properties of subgroups and homomorphisms, and they form the content of Chapter VI. The final chapter, on the universal covering group, could perhaps be most easily dispensed with, but, it is hoped, justifies its existence by bringing back into circulation Schreier's elegant method of constructing covering groups.
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Lie Groups and Compact Groups

Lie Groups and Compact Groups

John F. Price

Cambridge University Press
1977
pokkari
The theory of Lie groups is a very active part of mathematics and it is the twofold aim of these notes to provide a self-contained introduction to the subject and to make results about the structure of Lie groups and compact groups available to a wide audience. Particular emphasis is placed upon results and techniques which explicate the interplay between a Lie group and its Lie algebra, and, in keeping with current trends, a coordinate-free notation is used. Much of the general theory is illustrated by examples and exercises involving specific Lie groups.
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Lie Groupoids and Lie Algebroids in Differential Geometry

Lie Groupoids and Lie Algebroids in Differential Geometry

K. Mackenzie

Cambridge University Press
1987
pokkari
This book provides a striking synthesis of the standard theory of connections in principal bundles and the Lie theory of Lie groupoids. The concept of Lie groupoid is a little-known formulation of the concept of principal bundle and corresponding to the Lie algebra of a Lie group is the concept of Lie algebroid: in principal bundle terms this is the Atiyah sequence. The author's viewpoint is that certain deep problems in connection theory are best addressed by groupoid and Lie algebroid methods. After preliminary chapters on topological groupoids, the author gives the first unified and detailed account of the theory of Lie groupoids and Lie algebroids. He then applies this theory to the cohomology of Lie algebroids, re-interpreting connection theory in cohomological terms, and giving criteria for the existence of (not necessarily Riemannian) connections with prescribed curvature form. This material, presented in the last two chapters, is work of the author published here for the first time. This book will be of interest to differential geometers working in general connection theory and to researchers in theoretical physics and other fields who make use of connection theory.
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Lie Groups, Lie Algebras, Cohomology and some Applications in Physics

Lie Groups, Lie Algebras, Cohomology and some Applications in Physics

Josi A. de Azcárraga; Izquierdo Josi M.

Cambridge University Press
1995
sidottu
Now in paperback, this book provides a self-contained introduction to the cohomology theory of Lie groups and algebras and to some of its applications in physics. No previous knowledge of the mathematical theory is assumed beyond some notions of Cartan calculus and differential geometry (which are nevertheless reviewed in the book in detail). The examples, of current interest, are intended to clarify certain mathematical aspects and to show their usefulness in physical problems. The topics treated include the differential geometry of Lie groups, fibre bundles and connections, characteristic classes, index theorems, monopoles, instantons, extensions of Lie groups and algebras, some applications in supersymmetry, Chevalley-Eilenberg approach to Lie algebra cohomology, symplectic cohomology, jet-bundle approach to variational principles in mechanics, Wess-Zumino-Witten terms, infinite Lie algebras, the cohomological descent in mechanics and in gauge theories and anomalies. This book will be of interest to graduate students and researchers in theoretical physics and applied mathematics.
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Lie Algebras, Geometry, and Toda-Type Systems

Lie Algebras, Geometry, and Toda-Type Systems

Alexander V. Razumov; Mikhail V. Saveliev

Cambridge University Press
1997
pokkari
This book introduces the use of Lie algebra and differential geometry methods to study nonlinear integrable systems of Toda type. Many challenging problems in theoretical physics are related to the solution of nonlinear systems of partial differential equations. One of the most fruitful approaches in recent years has resulted from a merging of group algebraic and geometric techniques. The book gives a comprehensive introduction to this exciting branch of science. Chapters 1 and 2 review basic notions of Lie algebras and differential geometry with an emphasis on further applications to integrable nonlinear systems. Chapter 3 contains a derivation of Toda type systems and their general solutions based on Lie algebra and differential geometry methods. The last chapter examines explicit solutions of the corresponding equations. The book is written in an accessible ‘lecture note’ style with many examples and exercises to illustrate key points and to reinforce understanding.
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Lie Groups, Lie Algebras, Cohomology and some Applications in Physics

Lie Groups, Lie Algebras, Cohomology and some Applications in Physics

Josi A. de Azcárraga; Josi M. Izquierdo

Cambridge University Press
1998
pokkari
Now in paperback, this book provides a self-contained introduction to the cohomology theory of Lie groups and algebras and to some of its applications in physics. No previous knowledge of the mathematical theory is assumed beyond some notions of Cartan calculus and differential geometry (which are nevertheless reviewed in the book in detail). The examples, of current interest, are intended to clarify certain mathematical aspects and to show their usefulness in physical problems. The topics treated include the differential geometry of Lie groups, fibre bundles and connections, characteristic classes, index theorems, monopoles, instantons, extensions of Lie groups and algebras, some applications in supersymmetry, Chevalley-Eilenberg approach to Lie algebra cohomology, symplectic cohomology, jet-bundle approach to variational principles in mechanics, Wess-Zumino-Witten terms, infinite Lie algebras, the cohomological descent in mechanics and in gauge theories and anomalies. This book will be of interest to graduate students and researchers in theoretical physics and applied mathematics.
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