Sentence examples for be a smooth map from inspiring English sources

Let be a smooth map.

Let ( or ) be a smooth map.

Let be a smooth map from a Riemann surface.

Let be a smooth map and let be its projection.

Let ϕ : A → A be a smooth map and f : ( X, A ) → ( X, A ) be a smooth map whose restriction to A is ϕ.

Let be a smooth map and let be a -stable decomposition of, orthogonal with respect to.

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).

A stronger property than conformality is isotropy: if is a smooth map from a Riemann surface, is isotropic if [12] (2.13).

Suppose that ϕ : S 1 → S 1 is a smooth map defined by ϕ = ζ k for some k ≥ 2 and that f : ( S 2, S 1 ) → ( S 2, S 1 ) is a smooth extension of ϕ.

Theorem 5 Let ϕ : S n − 1 → S n − 1 be a sparse map of degree d and suppose f : ( B n, S n − 1 ) → ( B n, S n − 1 ) is a smooth map extending ϕ.

Theorem 10 Let n ≥ 2, and let ϕ : S n − 1 → S n − 1 be a sparse map of degree d and suppose f : ( B n, S n − 1 ) → ( R n, S n − 1 ) is a smooth map extending ϕ.