Sentence examples similar to extended manifold from inspiring English sources

This paper presents a general theoretical and computational framework, in which spline surfaces defined over planar domains can be systematically extended to manifold domains with arbitrary topology with or without boundaries.

Along with the integration, the functionality of the tools was also extended in manifold ways.

We used laminar premixed free flames to extend the manifolds generated with ILDM, thus leading to smooth and accurate evolutions of the species along all the flame front.

Especially in the latter scheme, a simple controller is designed via extending equilibrium manifolds of the origin system, which can stabilize the chaotic irregular states not only to arbitrary desired equilibrium-alike point but also to any target periodic orbits as designated online.

Based on this observer, a simple controller is designed via extending equilibrium manifolds of the original system, which can stabilize the chaotic irregular states not only to arbitrary desired equilibrium-alike points but also to any target periodic orbits as designated online.

Actually, many concepts and techniques fitting in Euclidean spaces have been extended to Riemannian manifolds.

The work of Gelfand and Fuks concerning the cohomology of the Lie algebra of all vector fields on a manifold is extended to the cohomology of the Lie algebra of all hamiltonian vector fields on a symplectic manifold.

The existence of extremals of the Moser-Trudinger inequality was also extended to compact Riemannian manifold cases by Li in [9, 10].

In this article, geodesic E-convex sets and geodesic E-convex functions on a Riemannian manifold are extended to the so-called geodesic strongly E-convex sets and geodesic strongly E-convex functions.

Melnikov's procedure for defining the criteria for transversal intersection of the stable and unstable manifolds is extended for the systems with fractional order deflection function.

For α = 0 we obtain a generalization of Wiener's theorem that had previously been extended to compact Riemannian manifolds by Michael Taylor.