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For all n, there exists a k such that the kth term of the Goodstein sequence G_k(n)=0. In other words, every Goodstein sequence converges to 0. The secret underlying ...

Given two groups G and H, there are several ways to form a new group. The simplest is the direct product, denoted G×H. As a set, the group direct product is the Cartesian ...

The group direct sum of a sequence {G_n}_(n=0)^infty of groups G_n is the set of all sequences {g_n}_(n=0)^infty, where each g_n is an element of G_n, and g_n is equal to the ...

The Killing form is an inner product on a finite dimensional Lie algebra g defined by B(X,Y)=Tr(ad(X)ad(Y)) (1) in the adjoint representation, where ad(X) is the adjoint ...

A lattice graph, also known as a mesh graph or grid graph, is a graph possessing an embedding in a Euclidean space R^n that forms a regular tiling. Examples include grid ...

Lattice theory is the study of sets of objects known as lattices. It is an outgrowth of the study of Boolean algebras, and provides a framework for unifying the study of ...

The Lorenz asymmetry coefficient is a summary statistic of the Lorenz curve that measures the degree of asymmetry of a Lorenz curve. The Lorenz asymmetry coefficient is ...

A monotonic function is a function which is either entirely nonincreasing or nondecreasing. A function is monotonic if its first derivative (which need not be continuous) ...

Given a set of ordered quantities, a list of the fractions of values at or below each quantity is know as a plotting position. A quantile-quantile plot compares observed ...

The signature of a non-degenerate quadratic form Q=y_1^2+y_2^2+...+y_p^2-y_(p+1)^2-y_(p+2)^2-...-y_r^2 of rank r is most often defined to be the ordered pair (p,q)=(p,r-p) of ...