Introduction To Element Theory

Describing a new and appealing way of analysing speech sounds, this book introduces you to the theory of elements in phonology. Traditional features are capable of describing segments and segmental patterns, but they are often unable to explain why those patterns are the way they are. By using elements to represent segmental structure, we begin to understand why languages show such a strong preference for certain kinds of segments, contrasts, phonological processes and sound changes. Using examples from a wide range of languages, this book demonstrates the process of analysing phonological data using elements, and gives readers the opportunity to compare element-based and feature-based accounts of the same phonological patterns. Backley also challenges traditional views through his innovative analysis of English weak vowels and diphthongs and hsi unified treatment of linking r and intrusive r as glide formation processes. Providing a thorough introduction to the main topics in segmental phonology, this is an excellent overview for both students with a background in standard phonology as well as for those who are new to the field.Key Features* Provides a full and up-to-date description of Element Theory * Includes examples from many languages and various dialects of English * Further reading suggested for each topic * Contains over 100 illustrations, including spectral and spectrographic figures

A fresh alternative for describing segmental structure in phonology

This introduction to the theory of Sobolev spaces and Hilbert space methods in partial differential equations is geared toward readers of modest mathematical backgrounds. It offers coherent, accessible demonstrations of the use of these techniques in developing the foundations of the theory of finite element approximations. J. T. Oden is Director of the Institute for Computational Engineering & Sciences (ICES) at the University of Texas at Austin, and J. N. Reddy is a Professor of Engineering at Texas A&M University. They developed this essentially self-contained text from their seminars and courses for students with diverse educational backgrounds. Their effective presentation begins with introductory accounts of the theory of distributions, Sobolev spaces, intermediate spaces and duality, the theory of elliptic equations, and variational boundary value problems. The second half of the text explores the theory of finite element interpolation, finite element methods for elliptic equations, and finite element methods for initial boundary value problems. Detailed proofs of the major theorems appear throughout the text, in addition to numerous examples.

Element Theory (ET) covers a range of approaches that consider privativity a central tenet defining the internal structure of segments. This volume provides an overview and extension of this program, exploring new lines of research within phonology and at its interface (phonetics and syntax). The present collection reflects on issues concerning the definition of privative primes, their interactions, organization, and the operations that constrain phonological and syntactic representations. The contributions reassess theoretical questions, which have been implicitly taken for granted, regarding privativity and its corollaries. On the empirical side, it explores the possibilities ET offers to analyze specific languages and phonological phenomena.

The main purpose of this book is to provide a simple and accessible introduction to the mixed finite element method as a fundamental tool to numerically solve a wide class of boundary value problems arising in physics and engineering sciences. The book is based on material that was taught in corresponding undergraduate and graduate courses at the Universidad de Concepcion, Concepcion, Chile, during the last 7 years. As compared with several other classical books in the subject, the main features of the present one have to do, on one hand, with an attempt of presenting and explaining most of the details in the proofs and in the different applications. In particular several results and aspects of the corresponding analysis that are usually available only in papers or proceedings are included here.

This Very Short Introduction traces the history and cultural impact of the elements on humankind, and examines why people have long sought to identify the substances around them. Looking beyond the Periodic Table, the author takes the reader on an engaging and entertaining tour: from the Greek philosophers who propounded a system with four elements - earth, air, fire, and water - to the modern-day scientists who are able to create their own.

This definitive introduction to finite element methods was thoroughly updated for this 2007 third edition, which features important material for both research and application of the finite element method. The discussion of saddle-point problems is a highlight of the book and has been elaborated to include many more nonstandard applications. The chapter on applications in elasticity now contains a complete discussion of locking phenomena. The numerical solution of elliptic partial differential equations is an important application of finite elements and the author discusses this subject comprehensively. These equations are treated as variational problems for which the Sobolev spaces are the right framework. Graduate students who do not necessarily have any particular background in differential equations, but require an introduction to finite element methods will find this text invaluable. Specifically, the chapter on finite elements in solid mechanics provides a bridge between mathematics and engineering.

This introductory exposition of group theory by an eminent Russian mathematician is particularly suited to undergraduates. Includes a wealth of simple examples, primarily geometrical, and end-of-chapter exercises. 1959 edition.