Search Results for ""

Regardless of where one white and one black square are deleted from an ordinary 8×8 chessboard, the reduced board can always be covered exactly with 31 dominoes (of dimension ...

G = int_0^infty(e^(-u))/(1+u)du (1) = -eEi(-1) (2) = 0.596347362... (3) (OEIS A073003), where Ei(x) is the exponential integral. Stieltjes showed it has the continued ...

A binomial coefficient (N; k) with k>=2 is called good if its least prime factor satisfies lpf(N; k)>k (Erdős et al. 1993). This is equivalent to the requirement that GCD((N; ...

Another name for the confluent hypergeometric function of the second kind, defined by where Gamma(x) is the gamma function and _1F_1(a;b;z) is the confluent hypergeometric ...

A decomposition of a module into a direct sum of submodules. The index set for the collection of submodules is then called the grading set. Graded modules arise naturally in ...

int_a^b(del f)·ds=f(b)-f(a), where del is the gradient, and the integral is a line integral. It is this relationship which makes the definition of a scalar potential function ...

The determinant G(f_1,f_2,...,f_n)=|intf_1^2dt intf_1f_2dt ... intf_1f_ndt; intf_2f_1dt intf_2^2dt ... intf_2f_ndt; | | ... |; intf_nf_1dt intf_nf_2dt ... intf_n^2dt|.

Given a set V of m vectors (points in R^n), the Gram matrix G is the matrix of all possible inner products of V, i.e., g_(ij)=v_i^(T)v_j. where A^(T) denotes the transpose. ...

Let f_1(x), ..., f_n(x) be real integrable functions over the closed interval [a,b], then the determinant of their integrals satisfies

The graph complement of a graph hole. Graph antiholes are called even if they have an even number of vertices and odd if they have an odd number of vertices (Chvátal). No odd ...