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This volume contains papers presented at the Twelfth Taniguchi
Symposium on the Theory of Condensed Matter, which was held at
Kashikojima (in Ise Shima National Park), Japan, November 14-19,
1989. The general purpose of the Taniguchi Symposia is to encourage
important developing, rather than established, fields in condensed
matter theory. The topic of the present sym posium, Quasicrystais,
is quite typical. In 1984, Shechtman, Blech, Gratias and Cahn
discovered the icosahedral symmetry of a diffraction pattern and
Levine and Steinhardt independently presented the notion of
quasicrystals. Before these discoveries, Roger Penrose of Oxford
University had invented a space-filling non-periodic tiling, now
called Penrose tiling. These factors form a new field that had
become mathematically viable by the end of 1984, and many important
new ideas are still being created. In standard textbooks of
solid-state science, the first chapter used to be devoted to
symmetry and periodicity in crystals. Now, the textbooks should be
revised; quasi-periodicity and its physical properties should be
added in several chapters and almost all standard conceptions
should be reconsidered. However, the facts that are known about
quasiperiodicity are not enough to complete even an introductory
chapter of a textbook. Revision should be extended to generalized
crystallography, defects, crystal growth, electronic structure,
spectral theory and localization, electron transport, spin
statistics, etc. These are all topics treated in this volume.
The basics of complex functions will be explained for students of
Engineering Sciences, with the aim of being able to use 'complex
function theory' as a tool. The goal is not rigor as mathematics,
but ease of use that may suit the application. Explanations are
based on concrete examples rather than abstract general theory. The
book starts from very beginning of complex numbers, and extends
theory of Introduction to Elliptic Function and Hypergeometric
Differential Equations.
The basics of complex functions will be explained for students of
Engineering Sciences, with the aim of being able to use 'complex
function theory' as a tool. The goal is not rigor as mathematics,
but ease of use that may suit the application. Explanations are
based on concrete examples rather than abstract general theory. The
book starts from very beginning of complex numbers, and extends
theory of Introduction to Elliptic Function and Hypergeometric
Differential Equations.
This book is aimed at researchers who are working in a field of
quasicrystals to provide a reference to recent developments and
ideas in the field and also at graduate students, who intend to
study quasicrystals, to provide introduction of ideas. Topics in
this book cover an entire field of quasicrystals, both experimental
and theoretical, including new developments: the state of the art
in quasicrystallography, new families of quasicrystals, phasons in
aperiodic solids, ab initio studies on stability mechanism, quantum
transport phenomena, elastic/plastic properties and surface of
quasicrystals.
. Comprehensive reviews by experts in the field
. Complete reference of original papers and new topics
. Intelligible introduction of quasicrystals by experts
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