# simplicial

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## simplicial

(sɪmˈplɪʃəl)
(Mathematics) relating to simplexes
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The anonymous computability theorem guarantees a simplicial map [Mu]: [Xi]([Tau]([S.
Z) denotes the simplicial complex of the universal covering of W and [[cross product].
Classification with Sparse Grids using Simplicial Basis Functions," Intelligent Data Analysis, 6, 483-502, 2002.
Although multiplier bimonoids in general are not known to correspond to comonoids in any monoidal category, we classify them in terms of maps from the Catalan simplicial set to another suitable simplicial set; thus they can be regarded as (co)monoids in something more general than a monoidal category (namely the simplicial set itself).
One then says a few words about the simplicial complexes attached to the quadrangulation, which can be thought of as the dual of Baryshnikov's Stokes polytopes.
Since the theory of hypergraphs is still too under-developed, we resort to geometry and topology, which view a graph as a one-dimensional simplicial complex.
For a graph G, x e V(G), if G[N(x)] is connected, then x is locally connected; if G[N(x)] is a complete induced subgraph of G, then x is simplicial; if x is locally connected, but not simplicial, then x is eligible.
This resembles the definition of weakly clique irreducible graphs [14], in which every edge should belong to a clique that contains a simplicial edge.
To formulate precise results, they introduce the setting of simplicial complexes with minimum degree sequences, which is a generalization of the usual minimum degree condition.
Selinger Simplicial cycles and the computation of simplicial trees J.
The characteristic features of these new methods are the following: (1) instead of homogeneous simplicial or hexahedral meshes, spatial discretizations which consist of arbitrary, even non-convex, polygons or polyhedra are admissible; (2) trial functions are constructed as local solutions of the partial differential equation with simple, usually piecewise linear boundary data on each element; (3) Green's formula then permits the reduction of the variational equation to the element boundaries, leading to a so-called skeletal variational formulation; (4) techniques based on boundary element methods (BEM) are used in order to approximate the Dirichlet-to-Neumann maps which are associated to the element-local problems.
Geometric aspects of the simplicial discretization of Maxwell's equations," Progress In Electromagnetics Research, Vol.

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