Titlebook: Mathematical Techniques in Crystallography and Materials Science; Edward Prince Book 2004Latest edition Springer-Verlag Berlin Heidelberg

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Estimation of Uncertainty,e data. We are then faced with the question, “How confident can we be that the parameters that give the best fit correspond to the facts concerning the physical or chemical quantities we were trying to measure?” This question resolves itself into the problem of estimating two distinct quantities, which we call . and ..

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978-3-540-21111-2Springer-Verlag Berlin Heidelberg 2004

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Tensors,stem. We can express this statement mathematically by saying that . = .·(.) = . . = ., a constant independent of coordinate systems. Or, in other words, the quantity . · (.) is invariant under all rotations of coordinate axes.

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Data Fitting,rameters. In this chapter we shall begin with a discussion of the form of the function . in somewhat greater detail than usually appears in treatments of model fitting, in order to highlight some of the assumptions that are made implicitly when a particular procedure is used. We shall then discuss v

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The Fast Fourier Transform,enting the problems caused by incomplete information make extensive use of iterative, trial-and-error computations whose efficiency can be greatly enhanced by the use of computational methods known as ., or FFTs.

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others seeking a dictionary of basic mathematical and crystallographic terms. The third edition further clarifies key points, as well as offers new sections on two topics: the projection matrix and the fast Fourier transform. .978-3-540-21111-2978-3-642-18711-7

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Mathematical Techniques in Crystallography and Materials Science

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Mathematical Techniques in Crystallography and Materials Science978-3-642-18711-7

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that ‘the real income per head of the “developed” countries, making allowance for shortcomings in statistical measurement, is 10, 20 or perhaps even 30 times as large as the real income per head of Asia, Latin America or South Eastern Europe’ (Kaldor 1956b, p. 20).