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A fractal curve, also called the C-curve (Gosper 1972). The base curve and motif are illustrated below. Duvall and Keesling (1999) proved that the Hausdorff dimension of the ...

The roots of a semisimple Lie algebra g are the Lie algebra weights occurring in its adjoint representation. The set of roots form the root system, and are completely ...

A link invariant defined for a two-component oriented link as the sum of +1 crossings and -1 crossing over all crossings between the two links divided by 2. For components ...

The second-order ordinary differential equation y^('')+g(y)y^('2)+f(x)y^'=0 (1) is called Liouville's equation (Goldstein and Braun 1973; Zwillinger 1997, p. 124), as are the ...

There are no fewer than three distinct notions of the term local C^*-algebra used throughout functional analysis. A normed algebra A=(A,|·|_A) is said to be a local ...

A semi-Riemannian manifold M=(M,g) is said to be Lorentzian if dim(M)>=2 and if the index I=I_g associated with the metric tensor g satisfies I=1. Alternatively, a smooth ...

Consider the local behavior of a map f:R^m->R^n by choosing a point x in R^m and an open neighborhood U subset R^m such that x in U. Now consider the set of all mappings ...

A maximal ideal of a ring R is an ideal I, not equal to R, such that there are no ideals "in between" I and R. In other words, if J is an ideal which contains I as a subset, ...

A function f:X->R is measurable if, for every real number a, the set {x in X:f(x)>a} is measurable. When X=R with Lebesgue measure, or more generally any Borel measure, then ...

1. Find a complete system of invariants, or 2. Decide when two metrics differ only by a coordinate transformation. The most common statement of the problem is, "Given metrics ...