curvilinear coordinates. This treatment includes in particular a direct proof of the three-dimensional Korn inequality in curvilinear coordinates. The fourth and last chapter, which heavily relies on Chapter 2, begins by a detailed description of the nonlinear and linear equations proposed by W.T. Koiter for modeling thin elastic shells. These equations are "two-dimensional", in the sense that they are expressed in terms of two curvilinear coordinates used for de?ning the middle surface of the shell. The existence, uniqueness, and regularity of solutions to the linear Koiter equations is then established, thanks this time to a fundamental "Korn inequality on a surface" and to an "in?nit- imal rigid displacement lemma on a surface". This chapter also includes a brief introduction to other two-dimensional shell equations. Interestingly, notions that pertain to di?erential geometry per se,suchas covariant derivatives of tensor ?elds, are also introduced in Chapters 3 and 4, where they appear most naturally in the derivation of the basic boundary value problems of three-dimensional elasticity and shell theory. Occasionally, portions of the material covered here are adapted from - cerpts from my book "Mathematical Elasticity, Volume III: Theory of Shells", published in 2000by North-Holland, Amsterdam; in this respect, I am indebted to Arjen Sevenster for his kind permission to rely on such excerpts. Oth- wise, the bulk of this work was substantially supported by two grants from the Research Grants Council of Hong Kong Special Administrative Region, China [Project No. 9040869, CityU 100803 and Project No. 9040966, CityU 100604].
This book collects papers mainly presented at the "International Conference on Partial Differential Equations: Theory, Control and Approximation" (May 28 to June 1, 2012 in Shanghai) in honor of the scientific legacy of the exceptional mathematician Jacques-Louis Lions. The contributors are leading experts from all over the world, including members of the Academies of Sciences in France, the USA and China etc., and their papers cover key fields of research, e.g. partial differential equations, control theory and numerical analysis, that Jacques-Louis Lions created or contributed so much to establishing.
This book addresses the application of Raman spectroscopic techniques to a range of diverse problems which arise in the study, conservation and restoration of artefacts and sites closely related to our cultural heritage as well as in authentication. These themes are naturally wider than what at first might be considered as artworks and archaeological artefacts and the topics include pigments, paintings, ceramics, glass, sculpture and patination / corrosion, textiles, industrial archaeology, the degradation and preservation of biomaterials, mummies and human skeletal remains. An interesting feature is the inclusion of modern case studies which describe specific problems and approaches to the Raman spectral analysis of items important to our cultural heritage. The text is prefaced with an introduction to the important parameters used in nondestructive Raman measurements and also highlights some future applications based upon novel miniaturised instrumentation for in-field studies and potential screening work which will identify specimens which would repay further studies in the laboratory. An attempt is made to give a snapshot of the state-of-the-art evolution since the beginning of the technique (1970s) and to point out potential further development. The book is co-edited by three international experts with many years' experience in the application of Raman spectroscopy to artworks, archaeological artefacts and in the investigation of materials and sites for cultural heritage preservation and each editor has undertaken to write individual chapters and different topics personally. The adopted approach is designed to convey the sort of information which has become available from the adoption of analytical Raman spectroscopy to different problems in the field of cultural heritage preservation through the spectral interrogation of artefacts and how the interpretation of the spectral data can assist museum curators, archaeologists and cultural heritage historians in the preservation and conservation of ancient materials and sites : a particular advantage in this respect is the ability of Raman spectroscopy to determine -generally in a strictly noninvasive procedure - at the laboratory or on-site with mobile instruments, the presence of both organic and inorganic components in a particular specimen together nondestructively without any chemical and mechanical pretreatment being undertaken, which is an essential requirement for rare and valuable samples . An important aside from this work is the means of spectral identification of ongoing biodeterioration and biological colonisation in specimens in storage and the effects of environmental deterioration such as humidity and temperature upon their integrity.
This contributed volume provides a critical review of research in the field of Electrochemical Promotion of Catalysis (EPOC). It presents recent developments during the past decade that have led to a better understanding of the field and towards applications of the EPOC concept. The chapters focus on the implementation of EPOC for developing sinter-resistant catalysts, catalysts for hydrogen production, ammonia production and carbon dioxide valorization. The book also highlights the developments towards electropromoted dispersed catalysts and for self-sustained electrochemical promotion which are currently expanding. This authoritative analysis of EPOC is useful for various scientific communities working at the interface of heterogeneous catalysis, solid state electrochemistry and materials science. It is of particular interest to groups whose research focuses on developments towards a better and more sustainable future.
