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Intuitively, a d-dimensional discrete percolation model is said to be long-range if direct flow is possible between pairs of graph vertices or graph edges which are "very ...

A function I_n(x) which is one of the solutions to the modified Bessel differential equation and is closely related to the Bessel function of the first kind J_n(x). The above ...

A polynomial discriminant is the product of the squares of the differences of the polynomial roots r_i. The discriminant of a polynomial is defined only up to constant ...

Zeros of the Riemann zeta function zeta(s) come in two different types. So-called "trivial zeros" occur at all negative even integers s=-2, -4, -6, ..., and "nontrivial ...

A secant line, also simply called a secant, is a line passing through two points of a curve. As the two points are brought together (or, more precisely, as one is brought ...

A variable is a symbol on whose value a function, polynomial, etc., depends. For example, the variables in the function f(x,y) are x and y. A function having a single ...

An automorphism of a graph is a graph isomorphism with itself, i.e., a mapping from the vertices of the given graph G back to vertices of G such that the resulting graph is ...

The antenna graph is the graph on 6 vertices illustrated above. It is implemented in the Wolfram Language as GraphData["AntennaGraph"].

The biconjugate gradient stabilized (BCGSTAB) method was developed to solve nonsymmetric linear systems while avoiding the often irregular convergence patterns of the ...

Cartesian coordinates are rectilinear two- or three-dimensional coordinates (and therefore a special case of curvilinear coordinates) which are also called rectangular ...