In studying the history of the vernacular in worship beginning with the Christian Scriptures, Dynamic Equivalence uncovers the power of a living language to transform communities of faith. How we pray when we come together for common worship has always been significant, but the issue of liturgical language received unprecedented attention in the twentieth century when Latin Rite Roman Catholic worship was opened to the vernacular at Vatican II. Worshiping in one's native tongue continues to be of issue as the churches debate over what type of vernacular should be employed. Dynamic Equivalence traces the history of liturgical language in the Western Christian tradition as a dynamic and living reality. Particular attention is paid to the twentieth century Vernacular Society within the United States and how the vernacular issue was treated at Vatican II, especially within an ecumenical context. The first chapter offers a short history of the vernacular from the first century through the twentieth. The second and third chapters contain a significant amount of archival material, much of which has never been published before. These chapters tell the story of a mixed group of Catholic laity and clergy dedicated to promoting the vernacular during the first half of the twentieth century. Chapter Four begins with a survey of vernacular promotion in the Reformation itself, explores the issue of vernacular worship as an instrument of ecumenical hospitality and concludes with some examples of ecumenical liturgical cooperation in the years immediately preceding the Council. The final chapter treats the vernacular debate at the Council with attention to the Vernacular Society's role in helping with theimplementation of the vernacular. Chapters are "A Brief History of the Vernacular," "The Origins of the Vernacular Society: 1946-1956," "Pressure for the Vernacular Mounts: 1956-1962," "Vernacular Worship and Ecumenical Exchange," "Vatican II and the Vindication of the Vernacular: 1962-1965" Keith F. Pecklers, SJ, SLD, is professor of liturgy at the Pontifical Gregorian University in Rome and professor of liturgical history at the Pontifical Liturgical Institute of Sant 'Anselmo. He is the author of The Unread Vision: The Liturgical Movement in the United States of America 1926-1955, and co-editor of Liturgy for the New Millennium: A Commentary on the Revised Sacramentary, published by The Liturgical Press.

Equivalence: Elizabeth L. Scott at Berkeley is the compelling story of one pioneering statistician’s relentless twenty-year effort to promote the status of women in academe and science. Part biography and part microhistory, the book provides the context and background to understand Scott’s masterfulness at using statistics to help solve societal problems. In addition to being one of the first researchers to work at the interface of astronomy and statistics and an early practitioner of statistics using high-speed computers, Scott worked on an impressively broad range of questions in science, from whether cloud seeding actually works to whether ozone depletion causes skin cancer. Later in her career, Scott became swept up in the academic women’s movement. She used her well-developed scientific research skills together with the advocacy skills she had honed, in such activities as raising funds for Martin Luther King Jr. and keeping Free Speech Movement students out of jail, toward policy making that would improve the condition of the academic workforce for women. The book invites the reader into Scott’s universe, a window of inspiration made possible by the fact that she saved and dated every piece of paper that came across her desk.

Drawing on a wide range of mathematical disciplines, including geometry, analysis, applied mathematics and algebra, this book presents an innovative synthesis of methods used to study problems of equivalence and symmetry which arise in a variety of mathematical fields and physical applications. Systematic and constructive methods for solving equivalence problems and calculating symmetries are developed and applied to a wide variety of mathematical systems, including differential equations, variational problems, manifolds, Riemannian metrics, polynomials and differential operators. Particular emphasis is given to the construction and classification of invariants, and to the reductions of complicated objects to simple canonical forms. This book will be a valuable resource for students and researchers in geometry, analysis, algebra, mathematical physics and other related fields.

Since the subject of Groups of Self-Equivalences was first discussed in 1958 in a paper of Barcuss and Barratt, a good deal of progress has been achieved. This is reviewed in this volume, first by a long survey article and a presentation of 17 open problems together with a bibliography of the subject, and by a further 14 original research articles.

This volume provides a self-contained introduction to some topics in orbit equivalence theory, a branch of ergodic theory. The first two chapters focus on hyperfiniteness and amenability. Included here are proofs of Dye's theorem that probability measure-preserving, ergodic actions of the integers are orbit equivalent and of the theorem of Connes-Feldman-Weiss identifying amenability and hyperfiniteness for non-singular equivalence relations. The presentation here is often influenced by descriptive set theory, and Borel and generic analogs of various results are discussed. The final chapter is a detailed account of Gaboriau's recent results on the theory of costs for equivalence relations and groups and its applications to proving rigidity theorems for actions of free groups.

Stimulus Equivalence for Students with Developmental Disabilities provides a step-by-step program for converting lesson plans into equivalence-based instruction. Using language and tools accessible to both students and practitioners, chapters present the concept of equivalence-based instruction and include clear and concise procedural descriptions, as well as data sheets and PowerPoint slides, with replaceable stimuli, so that special educators and clinicians will be able to immediately implement this procedure to teach any academic skill. Written in engaging prose with an emphasis on practical application, this book is an essential resource for special educators and graduate students studying to become BCBAs and special educators.