The assumption of differentiability can be weakened to continuity and one-sided differentiability of " f ".
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The problem with the above approach is that it relies on the differentiability of the objective function and on concavity.
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In terms of geometry, differentiability means that a curve is sufficiently smooth and can be approximated by a tangent.
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Continuity in the Eulerian description is expressed by the spatial and temporal continuity and continuous differentiability of the flow velocity field.
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The sole existence of partial derivatives satisfying the Cauchy Riemann equations is not enough to ensure complex differentiability at that point.
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This analysis of differentiability is usually given in terms of fractal dimension, with the Hausdorff dimension the most popular choice.
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There are a number of different types of differentiable manifolds, depending on the precise differentiability requirements on the transition functions.
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Also, usually differentiability or derivability are synonymous ( both in the F . and in the G . context ).
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If is of differentiability class, has continuous partial derivatives of all order and is called " smooth ".
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This approach assumes spatial and temporal continuity and even differentiability of locally defined intensive variables such as temperature and internal energy density.
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