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This volume contains a valuable collection of articles presented at a conference on Automorphic Forms and Zeta Functions in memory of Tsuneo Arakawa, an eminent researcher in modular forms in several variables and zeta functions. The book begins with a review of his works, followed by 16 articles by experts in the fields including H Aoki, R Berndt, K Hashimoto, S Hayashida, Y Hironaka, H Katsurada, W Kohnen, A Krieg, A Murase, H Narita, T Oda, B Roberts, R Schmidt, R Schulze-Pillot, N Skoruppa, T Sugano, and D Zagier. A variety of topics in the theory of modular forms and zeta functions are covered: Theta series and the basis problems, Jacobi forms, automorphic forms on Sp(1, q), double zeta functions, special values of zeta and L-functions, many of which are closely related to Arakawa's works. This collection of papers illustrates Arakawa's contributions and the current trends in modular forms in several variables and related zeta functions. Contents: Tsuneo Arakawa and His Works; Estimate of the Dimensions of Hilbert Modular Forms by Means of Differential Operator (H Aoki); Marsden-Weinstein Reduction, Orbits and Representations of the Jacobi Group (R Berndt); On Eisenstein Series of Degree Two for Squarefree Levels and the Genus Version of the Basis Problem I (S Bocherer); Double Zeta Values and Modular Forms (H Gangl et al.); Type Numbers and Linear Relations of Theta Series for Some General Orders of Quaternion Algebras (K Hashimoto); Skewholomorphic Jacobi Forms of Higher Degree (S Hayashida); A Hermitian Analog of the Schottky Form (M Hentschel & A Krieg); The Siegel Series and Spherical Functions on O(2n)/(O(n) x O(n)) (Y Hironaka & F Sati); Koecher-Maa Series for Real Analytic Siegel Eisenstein Series (T Ibukiyama & H Katsurada); A Short History on Investigation of the Special Values of Zeta and L-Functions of Totally Real Number Fields (T Ishii & T Oda); Genus Theta Series, Hecke Operators and the Basis Problem for Eisenstein Series (H Katsurada & R Schulze-Pillot); The Quadratic Mean of Automorphic L-Functions (W Kohnen et al.); Inner Product Formula for Kudla Lift (A Murase & T Sugano); On Certain Automorphic Forms of Sp(1,q) (Arakawa's Results and Recent Progress) (H Narita); On Modular Forms for the Paramodular Group (B Roberts & R Schmidt); SL(2,Z)-Invariant Spaces Spanned by Modular Units (N-P Skoruppa & W Eholzer). Readership: Researchers and graduate students in number theory or representation theory as well as in mathematical physics or combinatorics.
Method and Postmethod in Language Teaching provides a comprehensive, accessible, and engaging guide to the much-debated notions of ‘method’, ‘methods’, and ‘postmethod’ in language teaching. Divided into three sections − ‘Contexts’, ‘Concepts’, and ‘Debates’ – the book sets out ‘traditional’ understandings of method(s), examines alternative accounts and critiques that inform, and at times go beyond, postmethod thinking within language teaching, and finally relates these issues to key practical debates and dilemmas that teachers navigate in the classrooms. Highlighting the importance of teachers’ understandings of their own professional contexts, the volume uses the notion of method as a ‘lens’ through which teachers and other language teaching professionals can clarify their understandings of language teaching, both in terms of pedagogic practices and classroom possibilities, and with regard to the development of this diverse field more generally. Throughout, readers are encouraged to develop their own thinking and practice in contextually appropriate ways, supported by discussion questions and key readings that accompany each chapter, a glossary of key terms, and suggestions for additional reading. This book is an indispensable resource for language teachers and other language teaching professionals, as well as postgraduate and upper-level undergraduate students of Applied Linguistics, Language Teacher Education, and ELT/TESOL and other language teaching programmes.
Written by leading international experts, this handbook provides an accessible resource to task-based language teaching for teachers, as well as academic researchers. Chapters in the volume are presented in a reader-friendly style, with ideas made accessible through case studies, questions for discussion, and suggested further readings.
A comprehensive account of the research and practice of task-based language teaching.
Computational Techniques for Differential Equations
Twenty years ago, Dan Pearson was invited to make a garden at the 240- hectare Tokachi Millennium Forest in Hokkaido, Japan. Part of the intention was to entice city dwellers to reconnect with nature and improve land that had been lost to intensive agriculture, and this was achieved along with much more. By tuning into the physical and cultural essence of the place and applying a light touch in terms of cultivation, this world class designer has created a remarkable place which has its heart in Japan's long-held respect for nature and its head in contemporary ecological planting design. The bold, uplifting sweep of the Meadow Garden mixes garden plants with natives while the undulating landforms of the Earth Garden bring sculptural connection with the mountains beyond. Under the skillful custodianship of Midori Shintani, the garden has evolved beautifully to reflect principles that lie at the heart of Japanese culture: observation of seasonal changes, practical tasks carried out with care and an awareness of the interconnectedness of all living things. This beautiful, instructive book allows us all to experience something of the Tokachi effect, gain expert insights into how to plant gardens that feel right for their location, and reconnect with the land and wildlife that surround us.
This "hands-on" approach to the topic of arylation consolidates the body of key research over the last ten years (and up to around 2014) on various catalytic methods which involve an arylation process. Clearly structured, the chapters in this one-stop resource are arranged according to the reaction type, and focus on novel, efficient and sustainable processes, rather than the well-known and established cross-coupling methods. The entire contents are written by two authors with academic and industrial expertise to ensure consistent coverage of the latest developments in the field, as well as industrial applications, such as C-H activation, iron and gold-catalyzed coupling reactions, cycloadditions or novel methodologies using arylboron reagents. A cross-section of relevant tried-and-tested experimental protocols is included at the end of each chapter for putting into immediate practice, along with patent literature. Due to its emphasis on efficient, "green" methods and industrial applications of the products concerned, this interdisciplinary text will be essential reading for synthetic chemists in both academia and industry, especially in medicinal and process chemistry.