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Let (q_1,...,q_n,p_1,...,p_n) be any functions of two variables (u,v). Then the expression ...

A semi-Riemannian manifold M=(M,g) is said to be Lorentzian if dim(M)>=2 and if the index I=I_g associated with the metric tensor g satisfies I=1. Alternatively, a smooth ...

Low-dimensional topology usually deals with objects that are two-, three-, or four-dimensional in nature. Properly speaking, low-dimensional topology should be part of ...

A nonnegative function g(x,y) describing the "distance" between neighboring points for a given set. A metric satisfies the triangle inequality g(x,y)+g(y,z)>=g(x,z) (1) and ...

A predictor-corrector method for solution of ordinary differential equations. The third-order equations for predictor and corrector are y_(n+1) = ...

The wave equation in oblate spheroidal coordinates is del ^2Phi+k^2Phi=partial/(partialxi_1)[(xi_1^2+1)(partialPhi)/(partialxi_1)] ...

A system of curvilinear coordinates in which two sets of coordinate surfaces are obtained by revolving the parabolas of parabolic cylindrical coordinates about the x-axis, ...

A system of curvilinear coordinates. There are several different conventions for the orientation and designation of these coordinates. Arfken (1970) defines coordinates ...

A general set of methods for integrating ordinary differential equations. Predictor-corrector methods proceed by extrapolating a polynomial fit to the derivative from the ...

The index I associated to a symmetric, non-degenerate, and bilinear g over a finite-dimensional vector space V is a nonnegative integer defined by I=max_(W in S)(dimW) where ...