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Gray (1997) defines Bour's minimal curve over complex z by x^' = (z^(m-1))/(m-1)-(z^(m+1))/(m+1) (1) y^' = i((z^(m-1))/(m-1)+(z^(m+1))/(m+1)) (2) z^' = (2z^m)/m, (3) and then ...

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 most general form of Lagrange's group theorem, also known as Lagrange's lemma, states that for a group G, a subgroup H of G, and a subgroup K of H, (G:K)=(G:H)(H:K), ...

The Löwenheim-Skolem theorem is a fundamental result in model theory which states that if a countable theory has a model, then it has a countable model. Furthermore, it has a ...

In general, an arrangement of objects is simply a grouping of them. The number of "arrangements" of n items is given either by a combination (order is ignored) or permutation ...

A proper subgroup is a proper subset H of group elements of a group G that satisfies the four group requirements. "H is a proper subgroup of G" is written H subset G. The ...

A simple pole of an analytic function f is a pole of order one. That is, (z-z_0)f(z) is an analytic function at the pole z=z_0. Alternatively, its principal part is c/(z-z_0) ...

Let X(x)=X(x_1,x_2,...,x_n) be a random vector in R^n and let f_X(x) be a probability distribution on X with continuous first and second order partial derivatives. The Fisher ...

If A moves along a known curve, then P describes a pursuit curve if P is always directed toward A and A and P move with uniform velocities. Pursuit curves were considered in ...

The system of ordinary differential equations (dm)/(dt) = lambdamxm+gammax1 (1) (dgamma)/(dt) = lambdagammaxm. (2)