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O_h is the point group of symmetries of the octahedron having order 48 that includes inversion. It is also the symmetry group of the cube, cuboctahedron, and truncated ...

A prime ideal is an ideal I such that if ab in I, then either a in I or b in I. For example, in the integers, the ideal a=<p> (i.e., the multiples of p) is prime whenever p ...

The Riemann theta function is a complex function of g complex variables that occurs in the construction of quasi-periodic solutions of various equations in mathematical ...

A rooted graph is a graph in which one node is labeled in a special way so as to distinguish it from other nodes. The special node is called the root of the graph. The rooted ...

A unimodular matrix is a real square matrix A with determinant det(A)=+/-1 (Born and Wolf 1980, p. 55; Goldstein 1980, p. 149). More generally, a matrix A with elements in ...

A universal differential equation (UDE) is a nontrivial differential-algebraic equation with the property that its solutions approximate to arbitrary accuracy any continuous ...

Let x be a real number, and let R be the set of positive real numbers mu for which 0<|x-p/q|<1/(q^mu) (1) has (at most) finitely many solutions p/q for p and q integers. Then ...

The Newton-Cotes formulas are an extremely useful and straightforward family of numerical integration techniques. To integrate a function f(x) over some interval [a,b], ...

Unlike quadratic, cubic, and quartic polynomials, the general quintic cannot be solved algebraically in terms of a finite number of additions, subtractions, multiplications, ...

Vassiliev invariants, discovered around 1989, provided a radically new way of looking at knots. The notion of finite type (a.k.a. Vassiliev) knot invariants was independently ...