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Percolation, the fundamental notion at the heart of percolation theory, is a difficult idea to define precisely though it is quite easy to describe qualitatively. From the ...

A random-connection model (RCM) is a graph-theoretic model of continuum percolation theory characterized by the existence of a stationary point process X and a non-increasing ...

The geometric centroid (center of mass) of the polygon vertices of a triangle is the point G (sometimes also denoted M) which is also the intersection of the triangle's three ...

The Wigner 3j-symbols (j_1 j_2 j_3; m_1 m_2 m_3), also known as "3j symbols" (Messiah 1962, p. 1056) or Wigner coefficients (Shore and Menzel 1968, p. 275) are quantities ...

Define an antipode of a given graph vertex v_i as a vertex v_j at greatest possible graph distance from v_i. Then an antipodal graph is a connected graph in which each vertex ...

A plane curve discovered by Maclaurin but first studied in detail by Cayley. The name Cayley's sextic is due to R. C. Archibald, who attempted to classify curves in a paper ...

A chord of a graph cycle C is an edge not in the edge set of C whose endpoints lie in the vertex set C (West 2000, p. 225). For example, in the diamond graph as labeled ...

An exact sequence is a sequence of maps alpha_i:A_i->A_(i+1) (1) between a sequence of spaces A_i, which satisfies Im(alpha_i)=Ker(alpha_(i+1)), (2) where Im denotes the ...

When the elongated square pyramid with unit edge lengths (i.e., an equilateral obelisk) is truncated by a plane passing through opposite corners of its square base and the ...

A transformation that preserves angles and changes all distances in the same ratio, called the ratio of magnification. A similarity can also be defined as a transformation ...