Robert L. Bryant – författare

Finsler geometry generalises Riemannian geometry in the same sense that Banach spaces generalise Hilbert spaces. This book presents an expository account of seven important topics in Riemann-Finsler geometry, ones which have undergone significant development but have not had a detailed pedagogical treatment elsewhere. Each article will open the door to an active area of research, and is suitable for a special topics course in graduate-level differential geometry. The contributors consider issues related to volume, geodesics, curvature, complex differential geometry and parametrised jet bundles, and include a variety of instructive examples.

Finsler geometry generalises Riemannian geometry in the same sense that Banach spaces generalise Hilbert spaces. This book presents an expository account of seven important topics in Riemann-Finsler geometry, ones which have undergone significant development but have not had a detailed pedagogical treatment elsewhere. Each article will open the door to an active area of research, and is suitable for a special topics course in graduate-level differential geometry. The contributors consider issues related to volume, geodesics, curvature, complex differential geometry and parametrised jet bundles, and include a variety of instructive examples.

The misuse and abuse of prescription drugs has reached epidemic proportions in recent years, yet many individuals still believe, incorrectly, that their use is without risk. This book explores those risks as well as controversies surrounding this public health issue.Prescription drugs are powerful tools that can be used to treat a variety of ailments, from pain to anxiety to insomnia. Their potency and perceived safety also make them targets for abuse. The misuse of prescription drugs can have dire health consequences for individuals and high economic costs for society, among other dangers. A part of Greenwood's Health and Medical Issues Today series, this book identifies prescription drugs that are abused and the consequences such abuse can have for both individuals and society, and discusses the many questions relating to how to address this public health issue. Part I explores the current magnitude of the prescription drug abuse epidemic in the United States, which drugs are most frequently abused, how individuals obtain these medications, and the consequences of abuse. Part II delves into the controversies surrounding the topic, including the roles that doctors and "Big Pharma" play and legal issues regarding prosecution of prescription drug abusers. Part III provides a variety of useful materials, including case studies, a timeline of critical events, and a directory of resources.

The misuse and abuse of prescription drugs has reached epidemic proportions in recent years, yet many individuals still believe, incorrectly, that their use is without risk. This book explores those risks as well as controversies surrounding this public health issue.Prescription drugs are powerful tools that can be used to treat a variety of ailments, from pain to anxiety to insomnia. Their potency and perceived safety also make them targets for abuse. The misuse of prescription drugs can have dire health consequences for individuals and high economic costs for society, among other dangers. A part of Greenwood's Health and Medical Issues Today series, this book identifies prescription drugs that are abused and the consequences such abuse can have for both individuals and society, and discusses the many questions relating to how to address this public health issue. Part I explores the current magnitude of the prescription drug abuse epidemic in the United States, which drugs are most frequently abused, how individuals obtain these medications, and the consequences of abuse. Part II delves into the controversies surrounding the topic, including the roles that doctors and "Big Pharma" play and legal issues regarding prosecution of prescription drug abusers. Part III provides a variety of useful materials, including case studies, a timeline of critical events, and a directory of resources.

This book gives a treatment of exterior differential systems. It will in­ clude both the general theory and various applications. An exterior differential system is a system of equations on a manifold defined by equating to zero a number of exterior differential forms. When all the forms are linear, it is called a pfaffian system. Our object is to study its integral manifolds, i. e. , submanifolds satisfying all the equations of the system. A fundamental fact is that every equation implies the one obtained by exterior differentiation, so that the complete set of equations associated to an exterior differential system constitutes a differential ideal in the algebra of all smooth forms. Thus the theory is coordinate-free and computations typically have an algebraic character; however, even when coordinates are used in intermediate steps, the use of exterior algebra helps to efficiently guide the computations, and as a consequence the treatment adapts well to geometrical and physical problems. A system of partial differential equations, with any number of inde­ pendent and dependent variables and involving partial derivatives of any order, can be written as an exterior differential system. In this case we are interested in integral manifolds on which certain coordinates remain independent. The corresponding notion in exterior differential systems is the independence condition: certain pfaffian forms remain linearly indepen­ dent. Partial differential equations and exterior differential systems with an independence condition are essentially the same object.

This book gives a treatment of exterior differential systems. It will in­ clude both the general theory and various applications. An exterior differential system is a system of equations on a manifold defined by equating to zero a number of exterior differential forms. When all the forms are linear, it is called a pfaffian system. Our object is to study its integral manifolds, i. e. , submanifolds satisfying all the equations of the system. A fundamental fact is that every equation implies the one obtained by exterior differentiation, so that the complete set of equations associated to an exterior differential system constitutes a differential ideal in the algebra of all smooth forms. Thus the theory is coordinate-free and computations typically have an algebraic character; however, even when coordinates are used in intermediate steps, the use of exterior algebra helps to efficiently guide the computations, and as a consequence the treatment adapts well to geometrical and physical problems. A system of partial differential equations, with any number of inde­ pendent and dependent variables and involving partial derivatives of any order, can be written as an exterior differential system. In this case we are interested in integral manifolds on which certain coordinates remain independent. The corresponding notion in exterior differential systems is the independence condition: certain pfaffian forms remain linearly indepen­ dent. Partial differential equations and exterior differential systems with an independence condition are essentially the same object.

In the period since the original four volumes of Phillip Griffiths's Selecta were published (Selected Works of Phillip A. Griffiths with Commentary), Parts 1-4, Collected Works, Volume 18), Griffiths has continued to produce beautiful and important work. The current two-part publication brings Griffiths's Selecta up to date by including the majority of his recent articles, as well as two older papers on differential geometry whose length had precluded their inclusion in the original Selecta.The papers are organized along the three main topics: Differential Geometry and Hodge Theory (Part 5) and Algebraic Cycles (Part 6). In addition to his papers, Griffiths has been an author of a number of research monographs. To give the reader an overview of what these monographs contain, introductions to some of these are also included.

In the period since the original four volumes of Phillip Griffiths's Selecta were published (Selected Works of Phillip A. Griffiths with Commentary), Parts 1-4, Collected Works, Volume 18), Griffiths has continued to produce beautiful and important work. The current two-part publication brings Griffiths's Selecta up to date by including the majority of his recent articles, as well as two older papers on differential geometry whose length had precluded their inclusion in the original Selecta.The papers are organized along the three main topics: Differential Geometry and Hodge Theory (Part 5) and Algebraic Cycles (Part 6). In addition to his papers, Griffiths has been an author of a number of research monographs. To give the reader an overview of what these monographs contain, introductions to some of these are also included.

In the period since the original four volumes of Phillip Griffiths's Selecta were published (Selected Works of Phillip A. Griffiths with Commentary), Parts 1-4, Collected Works, Volume 18), Griffiths has continued to produce beautiful and important work. The current two-part publication brings Griffiths's Selecta up to date by including the majority of his recent articles, as well as two older papers on differential geometry whose length had precluded their inclusion in the original Selecta.The papers are organized along the three main topics: Differential Geometry and Hodge Theory (Part 5) and Algebraic Cycles (Part 6). In addition to his papers, Griffiths has been an author of a number of research monographs. To give the reader an overview of what these monographs contain, introductions to some of these are also included.

The DD6 Symposium was, like its predecessors DD1 to DD5 both a research symposium and a summer seminar and concentrated on differential geometry. This volume contains a selection of the invited papers and some additional contributions. They cover recent advances and principal trends in current research in differential geometry.

The DD6 Symposium was, like its predecessors DD1 to DD5 both a research symposium and a summer seminar and concentrated on differential geometry. This volume contains a selection of the invited papers and some additional contributions. They cover recent advances and principal trends in current research in differential geometry.

The misuse and abuse of prescription drugs has reached epidemic proportions in recent years, yet many individuals still believe, incorrectly, that their use is without risk. This book explores those risks as well as controversies surrounding this public health issue.Prescription drugs are powerful tools that can be used to treat a variety of ailments, from pain to anxiety to insomnia. Their potency and perceived safety also make them targets for abuse. The misuse of prescription drugs can have dire health consequences for individuals and high economic costs for society, among other dangers. A part of Greenwood's Health and Medical Issues Today series, this book identifies prescription drugs that are abused and the consequences such abuse can have for both individuals and society, and discusses the many questions relating to how to address this public health issue. Part I explores the current magnitude of the prescription drug abuse epidemic in the United States, which drugs are most frequently abused, how individuals obtain these medications, and the consequences of abuse. Part II delves into the controversies surrounding the topic, including the roles that doctors and "Big Pharma" play and legal issues regarding prosecution of prescription drug abusers. Part III provides a variety of useful materials, including case studies, a timeline of critical events, and a directory of resources.