Sentence examples for a smooth map from inspiring English sources

Let be a smooth map.

Let ( or ) be a smooth map.

Let be a Riemann surface and a smooth map.

Let be a smooth map from a Riemann surface.

Let be a smooth map and let be its projection.

Whitney proved that, generically, critical points of a smooth map are folds or cusps (Whitney, 1955).

Let (gamma(t)) be a smooth mapping such that (gamma(0)=0) and frac{d^{k}gamma(t)}{dt^{k}}Big| _{t=0}, quad k=1, 2, ldots (operatorname{span} mathbb{R}^{n}) (smooth mappings of finite type in a small neighborhood of the origin).

Since the mapping exp and Π are smooth, Exp| x is a smooth mapping.

The type of manifold involved here is defined by the zero level set of a smooth mapping u Rn↦R.

We present an approach for constructing finite-volume methods for flux-divergence forms to any order of accuracy defined as the image of a smooth mapping from a rectangular discretization of an abstract coordinate space.

Then, by [[22], p.9] (the proof given there for a smooth mapping still works for a C 1 -map), for each △ x ∈ T x G and any nontrivial smooth curve c : → G with c ( 0 ) = x and c ′ ( 0 ) = △ x, one has that f x ′ △ x = ( d d t ( f ∘ c ) ( t ) ) t = 0. (2.8).