Sentence examples for of manifold of from inspiring English sources

We can therefore hope that a verification of manifold of degenerate zero-dimensional modes reported here is experimentally feasible with the system of Figure 5. Figure 5 Optical design for a 1D coupled-cavity array with topological properties: a 1D periodic array of sinusoidally curved waveguides.

Additionally, he explored the relationship between quantum field theory and the differential topology of manifolds of two and three dimensions.

On this base, conjectures were made and a general theory produced, first by Poincaré and then by the American engineer-turned-mathematician Solomon Lefschetz, concerning the nature of manifolds of arbitrary dimension.

(1) A family of automorphisms of manifolds of general type (not necessarily minimal models) induces a family of automorphisms of canonical models.

Bishop and O'Neill [1] introduced the notion of warped product manifolds in order to construct a large variety of manifolds of negative curvature.

The following statement was proved by Fried [92] in the case of manifolds of constant negative curvature and conjectured (in an even more precise form) in [94, p.181] for more general manifolds.

The aim of this study was to explore the use of manifolding of microchannels for performance enhancement of plate heat exchangers for single-phase, low heat flux (process type) applications operating in a counter flow configuration.

The Kervaire invariant problem, about the existence of manifolds of Kervaire invariant 1 in dimensions 2k − 2 can be reduced to a question about stable homotopy groups of spheres.

In this role he delivered a series of lectures under the heading "A General Study of the Manifold Nature of Music", which introduced his students to a wide range of ancient and modern works.

Let the world avail of the manifold benefits of Yoga, meditation, Ayurveda and so many of Hindu civilization's bequests to humanity.

We see it as an additional cost in terms of an event, but it generates a good return because of the manifold extension of the audience we can reach.