Sentence examples for for a smooth map from inspiring English sources

For a smooth map (u:(M,g rightarrow (N,h)) between compact Riemannian manifolds ((M,g)) and ((N,h)) with Riemannian metrics g and h, respectively, following Ara [6] for an F-harmonic map (also see [7 10]), Asserda in [4] gave the following definition.

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).

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.

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

In Figure  3 we present a smoothed map of the prevalence of support for FGM/C in Kenya.

The minimization of the variability of the maps across space, that is, a preference for smooth maps.

The functional is defined based on the hypothesis that the activity of the units reflects only two simple constraints: The minimization of the variability of the maps across space, that is, a preference for smooth maps.