例句與造句

1. Generative modelling gains efficiency through the possibility of creating high-level shape operators from low-level shape operators.
2. Generative modelling gains efficiency through the possibility of creating high-level shape operators from low-level shape operators.
3. In general, the eigenvectors and eigenvalues of the shape operator at each point determine the directions in which the surface bends at each point.
4. Without reference to a particular orthonormal basis, the principal curvatures are the eigenvalues of the shape operator, and the principal directions are its eigenvectors.
5. The approach can be generally applied to any shape representation that provides a basic set of generating functions, called in this context'elementary shape operators '.
6. It's difficult to find shape operator in a sentence. 用shape operator造句挺難的
7. More generally, on a Riemannian manifold, the second fundamental form is an equivalent way to describe the shape operator ( denoted by S ) of a hypersurface,
8. In differential geometry, the two "'principal curvatures "'at a given point of a surface are the eigenvalues of the shape operator at the point.
9. The Gauss map can be defined ( globally ) if and only if the surface is orientable, in which case its differential of the Gauss map is called the shape operator.
10. Quantum gravoelectrodynamics is the field of scientific study concerning the properties of electrodynamics and general relativity viewed through the tools of differential geometry . ?The origins of quantum gravoelectrodynamics can be found in the research of Friedrich Gauss [ 1 ] [ 2 ] and Bernhard Riemann [ 2 ] . ?Their vision was a search to find a theory based on analysis and calculations that explained nature . ?In their work they found many mathematical tools which can be used to understand electrostatics, geometry and spacetime . ?A more modern conceptualization can be found in John Wheeler s " Geometrodynamics . " ?The central idea here is that gravitation and electromagnetism can be described in terms of geometry itself [ 3 ] . ?Quantum gravoelectrodynamics starting point is the Minkowskian idea of spacetime [ 4 ] . ?For general relativity analysis occurs in spacetime and one takes derivatives to derive the matelectric field, the matmagnetic field, mass, velocity, matter waves, matter radiation and the other element of classical analysis . ?The manifold here is the traditional spacetime with units of distance . ?For electrodynamics analysis occurs in pospotential spacetime in which one takes derivatives to derive traditional concepts like the electric field, the magnetic field, charge waves ( fka electromagnetic waves ), charge radiation ( fka electromagnetic radiation ), current and charge . ?The manifold here has units of distance times the square root of Newtons divided by Amperes . ?Tools from differential geometry like the shape operator, the first fundamental form, the second fundamental form and the third fundamental form are used to find normal curvature, principal curvature, Gaussian curvature and mean curvatures.