Titlebook: General Theory of Irregular Curves; A. D. Alexandrov,Yu. G. Reshetnyak Book 1989 Kluwer Academic Publishers 1989 convergence.differentiabl

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Rosa Maria Vitale,Pietro Amodeochet. Here we are going to dwell in detail on the definition of a curve with the aim of clarifying certain peculiarities that are important while discussing the theory of curves, and of presenting the definition of a curve in a more geometrical form as compared to the classical definition by M. Frec

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https://doi.org/10.1007/978-3-658-18708-8oints, i.e., a finite sequence of the points of ., such that . ≤ . ≤ .. Let us set .. The least upper boundary of the quantity s(.) on the set of all chains of the curve . is called a length of the curve . and is denoted as s(.). The curve . is termed rectifiable if its length is finite.

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,Solution of Algebraic Systems of Equations, Crofton, but it was in the papers by W. Blaschke and co-workers, published in the ‘thirties, that integral geometry was formulated as an independent branch of research. This field of geometry proved to be quite viable and is still attracting the attention of scholars. For a description of the histo

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Governing Equations of Fluid Dynamicsnce (. − 1) numbers of ., ., ... , . of the curvatures at the point of the curve. Let us set . where integration is carried out with respect to the arc length. The functions obtained in this way will be called integral curvatures of the curve. There arises a problem — to give such a definition of th

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Multi-Phase Models in Civil Engineering,The definition of a tangent to a curve given below is essentially the same as that given in courses of differential geometry.

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