Sentence examples for manifold with the from inspiring English sources

A complex manifold is just a real manifold with the additional specifiction of a local complex structure around each point.

Holmes has derived a criterion for the onset of chaos using Melnikov theory that is based upon the initial entanglement of the unstable manifold with the stable limit cycle.

A dedicated experimental test bench has been used to measure the travel time of the injected gas from the valve to the divertor subvolume, using a manifold with the same pipe length as envisaged for the actual ITER device and studying a wide range of gas mixtures and throughputs.

Let ((M^n, g)) be a Kähler manifold with the Kähler metric g.

Let be a noncompact Riemannian manifold with the boundary (possibly empty).

The Cartesian product has the natural structure of a Riemannian manifold with the scalar product (2.5).

The tapering manifold design is the opposite of the expanding manifold; with this design, the average current density and maximum pressure were slightly lower than the expanding manifold.

Numerical examples are presented which use pseudo-spectral methods to solve simple elliptic equations on multi-cube representations of manifolds with the topologies T3, S2×S1 and S3.

Examples are also presented of numerical solutions of simple hyperbolic equations on multi-cube manifolds with the topologies R×T3, R×S2×S1 and R×S3.

We establish various functorial properties of L2-analytic torsion and also compute it for odd-dimensional, closed, hyperbolic manifolds, with the help of results from Fried.

In this paper, we prove the Hamilton differential Harnack inequality for positive solutions to the heat equation of the Witten Laplacian on complete Riemannian manifolds with the CD(−K,m -condition, where m∈[n,∞) and K≥0 are two constants.