Sentence examples for simplex if from inspiring English sources

Proof: q* is in the interior of the simplex if and.

The fixed point (½,½,0) associated with normal physiology is unstable whenever β>1, being stable otherwise; the fixed point (½,0, ½) is a stable fixed point whenever β>1 or whenever β<1 but β+ δ>1; in this last situation, a saddle point arises in the interior of the simplex, located at Indeed, we easily prove the following Theorem: q* is in the interior of the simplex if β<1 and β+ δ>1.

Additionally, we say that a simplex has dimension p or is a p-simplex if it has a cardinality of (p+1).

Such a simplex is an n-dimensional object and we shall call it sometimes an n-simplex if we would like to emphasize its dimension.

Each facet of the original simplicial complex is represented by a node in the dual complex, and (k+1) nodes span a k-simplex if the corresponding (k+1) facets have at least a node in common.

Each facet of the original simplicial complex K is represented by a node in a new one (chi(K)), and (k+1) nodes in (chi(K)) span a k-simplex if the corresponding facets have at least one node (author) in common.

The clique complex of a graph is a simplicial complex that is defined as follows: The subset ({ x_{0},dots, x_{k}}) is a k-simplex if and only if every pair of vertices in ({x_{0},dots, x_{k}}) is connected by an edge.

Two simplicial complexes and are homeomorphic if there is a bijection between the set of the vertices of and of such that is a simplex of if and only if is a simplex of (see [7, page 128]).

We say that a complex K, with the vertices V ( K ) = ⋃ S ∈ K S has the fixed simplex property if for every simplicial map f : V ( K ) → V ( K ) there exists a simplex S ∈ K which is mapped onto itself, i.e., f(S) = S.

Mixture variables are naturally constrained between 0 and 1 and add up to a fixed total, say 1 (total mass fraction), i.e., the components of a mixture is confined in a regular simplex and, if linear constraints are imposed on these components, in a polytope within that simplex.

Several skin disorders, such as epidermolytic hyperkeratosis and epidermolysis bullosa simplex, occur if epidermis development is disrupted [ 91].