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Algebraic geometry is the study of geometries that come from algebra, in particular, from rings. In classical algebraic geometry, the algebra is the ring of polynomials, and ...

In algebra, a period is a number that can be written an integral of an algebraic function over an algebraic domain. More specifically, a period is a real number ...

An algebraic variety is a generalization to n dimensions of algebraic curves. More technically, an algebraic variety is a reduced scheme of finite type over a field K. An ...

Many authors (e.g., Mendelson 1963; Pervin 1964) use the term arcwise-connected as a synonym for pathwise-connected. Other authors (e.g., Armstrong 1983; Cullen 1968; and ...

The arf invariant is a link invariant that always has the value 0 or 1. A knot has Arf invariant 0 if the knot is "pass equivalent" to the unknot and 1 if it is pass ...

The associated Stirling numbers of the first kind d_2(n,k)=d(n,k) are defined as the number of permutations of a given number n having exactly k permutation cycles, all of ...

An atlas is a collection of consistent coordinate charts on a manifold, where "consistent" most commonly means that the transition functions of the charts are smooth. As the ...

Let {a_i}_(i=0)^(N-1) be a periodic sequence, then the autocorrelation of the sequence, sometimes called the periodic autocorrelation (Zwillinger 1995, p. 223), is the ...

The Balaban index J is a graph index defined for a graph on n nodes, m edges, and c connected components by J=m/(gamma+1)sum_((i,j) in E(G))(D_iD_j)^(-1/2), where gamma=m-n+c ...

Ball point picking is the selection of points randomly placed inside a ball. n random points can be picked in a unit ball in the Wolfram Language using the function ...