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The covariant derivative of the Riemann tensor is given by (1) Permuting nu, kappa, and eta (Weinberg 1972, pp. 146-147) gives the Bianchi identities ...

The bicommutant theorem is a theorem within the field of functional analysis regarding certain topological properties of function algebras. The theorem says that, given a ...

A coordinate system which is similar to bispherical coordinates but having fourth-degree surfaces instead of second-degree surfaces for constant mu. The coordinates are given ...

The symbol O(x), pronounced "big-O of x," is one of the Landau symbols and is used to symbolically express the asymptotic behavior of a given function. In particular, if n is ...

A system of curvilinear coordinates variously denoted (xi,eta,phi) (Arfken 1970) or (theta,eta,psi) (Moon and Spencer 1988). Using the notation of Arfken, the bispherical ...

The function defined by the contour integral J_(n,k)(z) =1/(2pii)int^((0+))t^(-n-1)(t+1/t)^kexp[1/2z(t-1/t)]dt, where int_((0+)) denotes the contour encircling the point z=0 ...

The nth root of the content of the set sum of two sets in n-dimensional Euclidean space is greater than or equal to the sum of the nth roots of the contents of the individual ...

Given a permutation {p_1,p_2,...,p_n} of {1,...,n}, the bumping algorithm constructs a standard Young tableau by inserting the p_i one by one into an already constructed ...

A bundle map is a map between bundles along with a compatible map between the base manifolds. Suppose p:X->M and q:Y->N are two bundles, then F:X->Y is a bundle map if there ...

Due to nonlinearities in weather processes, a butterfly flapping its wings in Tahiti can, in theory, produce a tornado in Kansas. This strong dependence of outcomes on very ...