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The slicing of a three-dimensional object by a plane (or more general slice).

The system of partial differential equations iu_t+u_(xx)+alphau_(yy)+betau|u|^2-uv=0 v_(xx)+gammav_(yy)+delta(|u|^2)_(yy)=0.

The desmic configuration is three-dimensional configuration of points consisting of three tetrads of points, each two of the tetrads of which are perspective from the four ...

Given a point set P={x_n}_(n=0)^(N-1) in the s-dimensional unit cube [0,1)^s, the star discrepancy is defined as D_N^*(P)=sup_(J in Upsilon^*)D(J,P), (1) where the local ...

The system of partial differential equations u_t = (u^2-u_x+2v)_x (1) v_y = (2uv+v_x)_x. (2)

A finite-dimensional Lie algebra all of whose elements are ad-nilpotent is itself a nilpotent Lie algebra.

A metric topology induced by the Euclidean metric. In the Euclidean topology of the n-dimensional space R^n, the open sets are the unions of n-balls. On the real line this ...

Euler integration was defined by Schanuel and subsequently explored by Rota, Chen, and Klain. The Euler integral of a function f:R->R (assumed to be piecewise-constant with ...

Since |(a+ib)(c+id)| = |a+ib||c+di| (1) |(ac-bd)+i(bc+ad)| = sqrt(a^2+b^2)sqrt(c^2+d^2), (2) it follows that (a^2+b^2)(c^2+d^2) = (ac-bd)^2+(bc+ad)^2 (3) = e^2+f^2. (4) This ...

A continuous real function L(x,y) defined on the tangent bundle T(M) of an n-dimensional smooth manifold M is said to be a Finsler metric if 1. L(x,y) is differentiable at ...