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Minimal surfaces are defined as surfaces with zero mean curvature. A minimal surface parametrized as x=(u,v,h(u,v)) therefore satisfies Lagrange's equation, ...

An algebraic manifold is another name for a smooth algebraic variety. It can be covered by coordinate charts so that the transition functions are given by rational functions. ...

For any system that seeks to minimize a function, only seven different local forms of catastrophe "typically" occur for four or fewer variables: 1. Fold catastrophe, 2. Cusp ...

The case of the Weierstrass elliptic function with invariants g_2=1 and g_3=0. In this case, the half-periods are given by (omega_1,omega_2)=(omega,iomega), where omega is ...

In the equianharmonic case of the Weierstrass elliptic function, corresponding to invariants g_2=0 and g_3=1, the corresponding real half-period is given by omega_2 = ...

The case of the Weierstrass elliptic function with invariants g_2=-1 and g_3=0. The half-periods for this case are L(1+i)/4 and L(-1+i)/4, where L is the lemniscate constant ...

"The" octahedral graph is the 6-node 12-edge Platonic graph having the connectivity of the octahedron. It is isomorphic to the circulant graph Ci_6(1,2), the cocktail party ...

Jacobi's imaginary transformations relate elliptic functions to other elliptic functions of the same type but having different arguments. In the case of the Jacobi elliptic ...

A function f is said to be an entire modular form of weight k if it satisfies 1. f is analytic in the upper half-plane H, 2. f((atau+b)/(ctau+d))=(ctau+d)^kf(tau) whenever [a ...

A recursive primality certificate for a prime p. The certificate consists of a list of 1. A point on an elliptic curve C y^2=x^3+g_2x+g_3 (mod p) for some numbers g_2 and ...