Sentence examples for manifold is given from inspiring English sources

Recall that the critical manifold is given by the set of equilibria of the layer problem.

The distance between two points on the manifold is given in terms of the lengths of curves between them.

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).

If he believed the apperceiving subject to be a collection of representations, it would be surprising for him to deny that anything manifold is given through my representation of it.

where the (l + 1 -dimensional centre manifold is now aligned with m ^ = 0. Hence, the flow on the (l + 1 -dimensional centre manifold is givenowy system (7).

We note that another natural generalization of both quaternionic and totally real submanifolds in a quaternionic Kähler manifold is given by quaternionic CR-submanifolds.

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.

An explicit representation of lower bounds for the spectra of Schrödinger operators with magnetic fields on σ-compact Riemannian manifolds is given, using the positivity of the Pauli Hamiltonian.

(4) A particular, but very explicit case of locally symmetric manifolds is given by the VIP : = Varieties isogenous to a product.

A basic example of our class of manifolds is given by the hyperbolic space ({mathbb {H}}^{n}), which can be viewed as the open unit ball in ({mathbb {R}}^n) with the metric begin{aligned} g=4{dw^2over (1-|w|^2)^2},quad win B_{{mathbb {R}}^n}(0,1).

The homoclinic orbit which connects a fixed point with itself and the corresponding stable and unstable manifolds are given in the closed analytical form.