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piecewise smooth (Definition)

A curve $ \alpha : [a, b] \rightarrow \mathbb{R}^{n}$ is said to be piecewise smooth if each component $ \alpha_{1}, \ldots, \alpha_{n}$ of $ \alpha$ has a bounded derivative $ \alpha_{i}' \quad (i = 1, \ldots, n)$ which is continuous everywhere in $ [a, b]$ except (possibly) at a finite number of points at which left- and right-sided derivatives exist.



"piecewise smooth" is owned by cvalente. [ full author list (2) | owner history (1) ]
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See Also: rectifiable curve

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Cross-references: rectifiable curve, rectifiable, right-sided derivatives, points, number, finite, continuous, derivative, bounded, component, curve
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This is version 4 of piecewise smooth, born on 2002-07-30, modified 2007-06-08.
Object id is 3236, canonical name is PiecewiseSmooth.
Accessed 6139 times total.

Classification:
AMS MSC51N05 (Geometry :: Analytic and descriptive geometry :: Descriptive geometry)

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