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Complex Analysis

A ball of radius 1.

The dimension e(G), also called the Euclidean dimension (e.g., Buckley and Harary 1988) of a graph, is the smallest dimension n of Euclidean n-space in which G can be ...

Let L=<L, v , ^ > and K=<K, v , ^ > be lattices, and let h:L->K. Then h is a lattice homomorphism if and only if for any a,b in L, h(a v b)=h(a) v h(b) and h(a ^ b)=h(a) ^ ...

The number of equivalent hyperspheres in n dimensions which can touch an equivalent hypersphere without any intersections, also sometimes called the Newton number, contact ...

A subset X subset Y is said to be bicollared in Y if there exists an embedding b:X×[-1,1]->Y such that b(x,0)=x when x in X. The map b or its image is then said to be the ...

Any n-dimensional Riemannian manifold can be locally embedded into an (n+1)-dimensional manifold with Ricci curvature Tensor R_(ab)=0. A similar version of the theorem for a ...

The edge set of a graph is simply a set of all edges of the graph. The cardinality of the edge set for a given graph g is known as the edge count of g. The edge set for a ...

A weighted graph in which the weights are equal to the Euclidean lengths of the edges in a specified embedding (Skiena 1990, pp. 201 and 252).

A curvature of a submanifold of a manifold which depends on its particular embedding. Examples of extrinsic curvature include the curvature and torsion of curves in ...