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A proper subset S^' of a set S, denoted S^' subset S, is a subset that is strictly contained in S and so necessarily excludes at least one member of S. The empty set is ...

The Rabinovich-Fabrikant equation is the set of coupled linear ordinary differential equations given by x^. = y(z-1+x^2)+gammax (1) y^. = x(3z+1-x^2)+gammay (2) z^. = ...

A subset M subset R^n is called a regular surface if for each point p in M, there exists a neighborhood V of p in R^n and a map x:U->R^n of an open set U subset R^2 onto V ...

A right trapezoid is a trapezoid having two right angles. As illustrated above, the area of a right trapezoid is A = ah_2-1/2(h_2-h_1)a (1) = 1/2a(h_1+h_2). (2) A right ...

A seminorm is a function on a vector space V, denoted ||v||, such that the following conditions hold for all v and w in V, and any scalar c. 1. ||v||>=0, 2. ||cv||=|c|||v||, ...

Separation of variables is a method of solving ordinary and partial differential equations. For an ordinary differential equation (dy)/(dx)=g(x)f(y), (1) where f(y)is nonzero ...

The angles S_1=A_1/2 and S_2=A_2/2 obtained from solving sin(x+omega)=2sinomega (1) for x=A_1,A_2, where omega is the Brocard angle. The half-angles A_1 and A_2 are given by ...

A relation < is a strict order on a set S if it is 1. Irreflexive: a<a does not hold for any a in S. 2. Asymmetric: if a<b, then b<a does not hold. 3. Transitive: a<b and b<c ...

A surface in 3-space can be parameterized by two variables (or coordinates) u and v such that x = x(u,v) (1) y = y(u,v) (2) z = z(u,v). (3) If a surface is parameterized as ...

A tetractys, also called a tetraktys or decad, is an arrangement of 10 points in the form of a triangle with 1 point in the first row, two in the second, three in the third, ...