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Delta(x_1,...,x_n) = |1 x_1 x_1^2 ... x_1^(n-1); 1 x_2 x_2^2 ... x_2^(n-1); | | | ... |; 1 x_n x_n^2 ... x_n^(n-1)| (1) = product_(i,j; i>j)(x_i-x_j) (2) (Sharpe 1987). For ...

A weak pseudo-Riemannian metric on a smooth manifold M is a (0,2) tensor field g which is symmetric and for which, at each m in M, g_m(v_m,w_m)=0 for all w_m in T_mM implies ...

A weak Riemannian metric on a smooth manifold M is a (0,2) tensor field g which is both a weak pseudo-Riemannian metric and positive definite. In a very precise way, the ...

There are at least two theorems known as Weierstrass's theorem. The first states that the only hypercomplex number systems with commutative multiplication and addition are ...

A weighted adjacency matrix A_f of a simple graph is defined for a real positive symmetric function f(d_i,d_j) on the vertex degrees d_i of a graph as ...

Spinor fields describing particles of zero rest mass satisfy the so-called zero rest mass equations. Examples of zero rest mass particles include the neutrino (a fermion) and ...

Turing machines are defined by sets of rules that operate on four parameters: (state, tape cell color, operation, state). Let the states and tape cell colors be numbered and ...

A matching, also called an independent edge set, on a graph G is a set of edges of G such that no two sets share a vertex in common. It is not possible for a matching on a ...

The Pell numbers are the numbers obtained by the U_ns in the Lucas sequence with P=2 and Q=-1. They correspond to the Pell polynomial P_n(x) and Fibonacci polynomial F_n(x) ...

A dozen dozen, also called a gross. 144 is a square number and a sum-product number.