Sentence examples for extension of fields from inspiring English sources

(1) If k ′ / k is a finite extension of fields, the projective system ( Q y, n Γ ( k ′ ) ) n ≥ 1 has surjective transitions maps.

In order to judge the contribution of the extension of field trials to the accuracy of prediction of genomic selection, cross-validation across genotype was performed separately within population A and population B for grain yield and plant height based on increasing numbers of environments, that is, location-year combinations (CVG Env; Figure  3).

Like its scalar counterparts it should be a powerful tool in the inversion, approximation and extension of bandlimited fields on the sphere: vector fields such as gravity and magnetism in the earth and planetary sciences, or electromagnetic fields in optics, antenna theory and medical imaging.

The drastic changes in the production method and material form have also resulted in significant extension of application fields of glassy alloys.

Furthermore, since the extension of residue fields (overline{K}_w/overline{F}_v) is also separable of degree (d) (in particular, (w vert v) is unramified), by [25, Corollary 2.17], (mathcal O _{K, w}) is a separable (mathcal O _{F, v} -algebra.

A new key step in our construction is the systematic use of a Kählerian diffusion on the space of Jordan curves for which the welding functional gives rise to conformal martingales, together with a Douady Earle type conformal extension of vector fields on the circle to the disk.

Part of the recovery was the extension of rice fields in the northeastern region of the Mengwi kingdom which involved the building of dams, tunnels and temples.

As far as can be determined, extension of irrigated fields did not automatically result in the establishment of (semi) autonomous local irrigation units, or subak, which operated independently from villages.

In this book is considered, as the author writes, one of the most interesting questions of the Potential plane field theory, a possibility of an analytic extension of the field into the domain occupied by sources.

She reduced this to "Noether's problem", which asks whether the fixed field of a subgroup G of the permutation group Sn acting on the field k x1,..., xn) always is a pure transcendental extension of the field k. (She first mentioned this problem in a 1913 paper, where she attributed the problem to her colleague Fischer).

Instead of determining the Galois group of transformations of a given field and its extension, Noether asked whether, given a field and a group, it always is possible to find an extension of the field that has the given group as its Galois group.