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OverviewThis book summarises important outcomes of a quarter century of developments in advanced mathematical approaches and their implementations for deconvolution. The analysis of electron and relaxation time spectra obtained from the results of appropriate physical experiments fulfilled on real samples of bulk amorphous/crystalline semiconductors and insulators as well as on nano-structured materials and devices are also discussed. The second chapter of this book depicts key features of many well-known traditional and some modern techniques for experimental investigations of electron density and time relaxation spectra in such semiconductors and insulators. as Additionally, there is an emphasis on archetypal problems related to the analysis and interpretation of the results of those experimental techniques. Some generic (though crucially important in the context of this book) physical and mathematical aspects of the polarisation and relaxation processes in solids, well-known one-dimensional direct and inverse integral transforms, linear integral equations of the first and second kinds, ill-posed mathematical problems and specific mathematical approaches to solution(s) of those are discussed in the third, fourth and fifth chapters, respectively. A majority of the aforementioned mathematical approaches are essentially based on the so-called regularisation concept, pioneered by famous Russian mathematicians (A N Tikhonov, M M Lavrentiev, V K Ivanov, V Ya Arsenin and their co-workers) in the second half of the twentieth century. Mathematical aspects of the regularisation concept are discussed (to some extent) in the fifth chapter of the book in comparison to the similar aspects of the traditional modelling approach with multiple references on appropriate original articles and books. Thanks to distinctive features of the regularisation concept, it endures a protracted history (which nowadays well exceeds 5 decades), becomes the dominant strategy for the solution of various inverse problems, and is widely used in many types of modern applications and computational packages. In particular, the regularisation algorithms are incorporated into Mathematica, Matlab, Python and Octave packages. This generic regularisation concept had been successfully implemented by the author of this book during the development and practical realisation (programming) of several essentially different regularisation algorithms (described in detail in the sixth chapter of the book) for unambiguous investigations and the analysis of results of appropriated physical experiments, fulfilled over a period from 1984 to 2009, both in Russia and in Singapore. Furthermore, actual results of such experimental investigations are discussed in the seventh chapter following closely appropriate original publications, and in comparison with their counterparts obtained by traditional (eg: modelling) approaches. As it is also demonstrated in the seventh chapter with the relevant examples and detailed discussion(s), the implementation of the aforementioned regularisation algorithms allows one to identify (and interpret thereafter) new important features of the intra-gap and near-band-gap electronic spectra of the amorphous and polycrystalline semiconductors and insulators. The relaxation time spectra of those materials, which are usually unattainable via the implementation of the modelling approach is also analysed. It is important that the regularisation concept (mathematically related to its alternative ones, e.g., the direct and inverse Radon integral transforms) has many other, very important implementations, e.g., in medical computerised tomography, security-related applications, archaeology, geophysics, etc. Similar to the abovementioned spectroscopic techniques, the X-ray-based computerised tomography eventually yields vital information on features of electron density distribution in a studied object, though the desired function in the latter case rather depends on spatial variables than on energetic ones. The mathematical essence of the Radon-transform-based computerised tomography is also summarised very briefly in one of the sections of this book. A comprehensive reference list of this book comprises many other key references (for those who are interested in the aforementioned topics discussed herein). Full Product DetailsAuthor: Valeri LigatchevPublisher: Nova Science Publishers Inc Imprint: Nova Science Publishers Inc Weight: 0.586kg ISBN: 9781536125665ISBN 10: 1536125660 Pages: 362 Publication Date: 01 October 2017 Audience: College/higher education , Professional and scholarly , Tertiary & Higher Education , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In stock We have confirmation that this item is in stock with the supplier. It will be ordered in for you and dispatched immediately. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |