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In vector calculus, a complex lamellar vector field is a vector field which is orthogonal to a family of surfaces. In the broader context of differential geometry, complex lamellar vector fields are more often called hypersurface-orthogonal vector fields. They can be characterized in a number of different ways, many of which involve the curl.
In relativistic cosmology, Weyl's postulate stipulates that in the Friedmann model of the universe (a fluid cosmological model), the wordlines of fluid particles (modeling galaxies) should be hypersurface orthogonal. Meaning, they should form a 3-bundle of non-intersecting geodesics orthogonal to a series of spacelike hypersurfaces (hyperslices ...
A hypersurface in a (Euclidean, affine, or projective) space of dimension two is a plane curve. In a space of dimension three, it is a surface. For example, the equation + + + = defines an algebraic hypersurface of dimension n − 1 in the Euclidean space of dimension n.
An orthogonal array is simple if it does not contain any repeated rows. (Subarrays of t columns may have repeated rows, as in the OA(18, 7, 3, 2) example pictured in this section.) An orthogonal array is linear if X is a finite field F q of order q (q a prime power) and the rows of the array form a subspace of the vector space (F q) k. [2]
The Gauss map can be defined for hypersurfaces in R n as a map from a hypersurface to the unit sphere S n − 1 ⊆ R n. For a general oriented k - submanifold of R n the Gauss map can also be defined, and its target space is the oriented Grassmannian G ~ k , n {\displaystyle {\tilde {G}}_{k,n}} , i.e. the set of all oriented k -planes in R n .
Stomach pain or tummy troubles are among the most common ailments that affect children and adults alike. Feelings of bloating, cramping, constipation or nausea often occur because of something ...
Here, saying that = is irrotational means that the vorticity tensor of the corresponding timelike congruence vanishes; thus, this Killing vector field is hypersurface orthogonal. The fact that the spacetime admits an irrotational timelike Killing vector field is in fact the defining characteristic of a static spacetime .
And I like that we're changing [who is] considered [a] role model for kids,” she said. Disney/Eric McCandless. Ilona Maher and Alan Bersten on the 'Dancing with the Stars' semifinals on Nov. 19.