The dimension of a simplex [sigma] [member of] S(K) is defined as dim ([sigma]) = [absolute value of [sigma]]-1: simplices consisting of a single element are zero-dimensional, and simplices consisting of two elements are one-dimensional and so on.

On higher simplices the degeneracy maps are determined by the uniqueness of the filler for a given boundary.

Proof: The left hand side is counting simplices in the simplicial complex [G.sub.Q], with a marked initial inner edge.

They are of the same optimal order as a standard finite element method on an auxiliary finer mesh consisting of simplices.

People who speak, in Christianity, are aware that they are responsible for the salvation of all: of all the people (populus), of course, but especially of the humblest among the people (simplices, rudes, vulgus) ...

In addition, these simplices can be given color or texture attributes.

[94] used elementary computational-geometry operations such as, facet-segment intersection, point containment in simplices, and edge recovery in a plane, to produce high-level Boolean operations.

Let [DELTA](B[X, Y)) be the order complex of the poset B[X, Y]\{y}: it is the simplicial complex whose vertex set is B[X, Y]\{y} and whose simplices are the finite chains in the poset.

The topics include intersection multiplicity numbers between tropical hypersurfaces, elliptical curves in honeycomb form, tropically unirational varieties, categorical notions of layered tropical algebra and geometry, some acyclic systems of permutations that are not realizable by triangulations of a product of simplices, and tropical (1,1)-homology for floor decomposed surfaces.

Apta enim diligentia necessario requititur, quia secus termini peremptorii utiles simplices fideles p errar o urgerent, facile pessumdatis legibus quae terminos peremptorios statuunt".

Yamamoto, "A variable dimension fixed point algorithm and the orientation of simplices," Mathematical Programming, vol.

Liu, "On a notion of data depth based on random simplices," Annals of Statistics, vol.18, pp.405-414, 1990.