Sentence examples for manifold could be from inspiring English sources
Thurston proposed that every three-dimensional manifold could be broken down into one or more of eight types of component, including a spherical type.
The theory behind the Grassmann kernel would be helpful to understand how points on the manifold could be measured.
In 1873, Schläfli conjectured that every Riemann manifold could be locally considered as a submanifold of an Euclidean space with sufficient high codimension.
In 2008, it was proposed that a Sierpinsi manifold could be an alternative to the leaves of trees to cool down warming cities by discovering the fractal similarity of the former and the latter.
Soon after Riemann (1854) introduced the notion of a manifold, Schläfli (1873) conjectured that every Riemannian manifold could be locally considered as a submanifold of an Euclidean space with sufficiently high codimension.
It is found that for a design with straight-channels, water in the outflow manifold could be easily blocked by air/water streams from the gas flow channels; the airflow could be severely blocked even if there was only a small amount of water in the gas flow channels.
He argued that, while the manifolds could be made to take on many different shapes, they nonetheless had a "preferred" geometry, just as a piece of silk draped over a dressmaker's mannequin takes on the mannequin's form.
Poincaré took up the task and looked for ways in which such manifolds could be distinguished, thus opening up the whole subject of topology, then known as analysis situs.
The vessels were specially fabricated so that the existing racks, feed/product headers and manifolds could be utilized as they were already fabricated and installed.
Remark 3.2 This kind of integral manifolds could be used in the investigation of stability of systems of difference equations (see [15, 16]).
We divide our discussion into two scenarios, the near-field and far-field cases, and describe how the manifold lifting algorithm could be applied to these scenarios.
