Sentence examples for manifold given from inspiring English sources

Theorem 3.1 If any solution of the linear differential equation (19) with coefficients bounded together with their derivatives up to order p satisfies (3) on ℝ, then the linear system of differential equations (4) has the integral manifold given by (6), where K ( t ) is a p m × q m matrix.

The above property in 2 1 spatial manifold gives us sufficient conditions to carry out space-time beamforming.

A single manifold gives the possibility to analyse either Fe(II) or ΣFe [Fe(II) + Fe III)] in situ, or ΣFe in the lab on hydrothermal seawater samples.

The asymptotic behavior of the heat kernel of a Riemannian manifold gives rise to the classical concepts of parabolicity, stochastic completeness (or conservative property) and Feller property (or C0-diffusion property).

We then extend them to Riemannian manifolds, giving a sequence of inequalities which are equivalent to the curvature dimension inequality, and interpolate between this inequality and the Poincaré inequality for the invariant measure.

Instead, two different versions of string theory called type IIA string theory and type IIB can be compactified on completely different Calabi Yau manifolds giving rise to the same physics.

For 1 and 4 the ligand field manifolds that stem from the atomic F ground state manifold are given as solid sticks above or below the respective spectra.

Also, in §16 Kant remarks: "through the 'I', as simple representation, nothing manifold is given; only in intuition, which is distinct from the 'I', can a manifold be given" (B135).

The associated threshold manifold is given as the concatenation of the middle branch of the critical manifold and the fast fiber through the lower fold point, shown in Fig. 11.

In the singular limit, this manifold is given by the concatenation of the middle branch of the one-dimensional critical manifold and the fast fibre through a fold point when I app = 0 (see Fig. 11).

The quasiequilibrium manifold is given by the equations and for small ε it serves as an approximation to a slow manifold.