ELECTRICAL AND GEOMETRICAL PROPERTIES OF ORGANIC M

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This book addresses the physical mechanisms involved in the characteristic electrical properties and the geometrical structures that are observed from dipolar monolayers composed of organic molecules by using dielectric physics, electrostatics, the physics of liquid crystal, and soft matter physics. The orientational order parameters, introduced to quantify the orientational structures of monolayers, guide us towards this goal. Dielectric polarizations are spontaneously generated from monolayers because of their orientational structures, and electrostatic energies due to these dielectric polarizations play a key role in forming the geometrical structures that are observed from monolayers. Free energy minimization is a powerful tool to understand the physical mechanisms that stabilize these geometrical structures because of the soft matter nature of monolayers. The approach using mathematical differential geometry method makes this book unique among the literatures of monolayers. Sample Chapter(s) Preface Chapter 1: Introduction Contents: Introduction Dielectric Physics of Monolayers; Theory of Dielectric Polarization of Monolayers Dielectric Physics of Monolayers: Experimental Techniques to Measure Dielectric Polarizations of Monolayers Liquid Crystalline Properties of Monolayers on Water Surface Differential Geometry Method for Analyzing Domain Shapes Differential Geometry Method for Analyzing Domain Shapes II Comprehensive Approach for Analyzing Domain Shapes Readership: This book would be useful for physicists, chemists, biologists and electronic engineers of the field to understand their experimental results and to develop new theories.

GEOMETRIC GEMS (V2)

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Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on at school. The quadrilateral, one of the basic instruments in geometry, has a plethora of unexpected curiosities. The authors present these in an easily understood fashion, requiring nothing more than the very basics of school geometry to appreciate these curiosities and their justifications or proofs. The book is intended to be widely appreciated by a general audience, and their love for geometry should be greatly enhanced through exploring these many unexpected relationships in geometry. Geometric Gems is also suitable for mathematics teachers, to enhance the education of their students with these highly motivating quadrilateral properties. Request Inspection Copy Sample Chapter(s) Introduction Contents: About the Authors Acknowledgments Introduction Quadrilateral Curiosities Proofs of Quadrilateral Curiosities Toolbox Index Readership: The book is intended for the general readership, mathematics teachers, and mathematicians interested in extending their appreciation for geometry.

Geometric Gems: An Appreciation for Geometric Curiosities Volume I: The Wonders of Triangles

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【簡介】 Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on in school curriculums. The triangle, one of the basic instruments in geometry, has a plethora of unexpected curiosities. Geometric Gems presents one of the largest collections of triangle curiosities currently available, which the authors discuss in an easily understood fashion, requiring nothing more of readers other than the very basics of school geometry to appreciate these curiosities and their justifications or proofs. The book is intended to be widely appreciated by a general audience, and their love for geometry should be greatly enhanced through exploring these many unexpected relationships in geometry. Geometric Gems is also suitable for mathematics teachers, to enhance the education of their students with these highly motivating triangle properties. 【目錄】

Geometric Analysis on Real Analytic Manifold

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This monograph provides some useful tools for performing global geometric analysis on real analytic manifolds. At the core of the methodology of the book is a variety of descriptions for the topologies for the space of real analytic sections of a real analytic vector bundle and for the space of real analytic mappings between real analytic manifolds. Among the various descriptions for these topologies is a development of geometric seminorms for the space of real analytic sections. To illustrate the techniques in the book, a number of fundamental constructions in differential geometry are shown to induce continuous mappings on spaces of real analytic sections and mappings. Aimed at researchers at the level of Doctoral students and above, the book introduces the reader to the challenges and opportunities of real analytic analysis and geometry.