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y^('')-mu(1-1/3y^('2))y^'+y=0, where mu>0. Differentiating and setting y=y^' gives the van der Pol equation. The equation y^('')-mu(1-y^('2))y^'+y=0 with the 1/3 replaced by ...

The binary quadratic form F=<a,b,c> is said to be reduced if the following conditions hold. Let D=b^2-4ac be the discriminant, then 1. If D is negative, F is reduced if ...

A strict order > on the set of terms of a term rewriting system is called a reduction order if 1. The set of terms is well ordered with respect to >, that is, all its ...

A real-valued univariate function f=f(x) is said to have a removable discontinuity at a point x_0 in its domain provided that both f(x_0) and lim_(x->x_0)f(x)=L<infty (1) ...

Let R be the class of expressions generated by 1. The rational numbers and the two real numbers pi and ln2, 2. The variable x, 3. The operations of addition, multiplication, ...

A ruled surface is called a right conoid if it can be generated by moving a straight line intersecting a fixed straight line such that the lines are always perpendicular ...

A ring in the mathematical sense is a set S together with two binary operators + and * (commonly interpreted as addition and multiplication, respectively) satisfying the ...

The Schur decomposition of a complex square matrix A is a matrix decomposition of the form Q^(H)AQ=T=D+N, (1) where Q is a unitary matrix, Q^(H) is its conjugate transpose, ...

The semigroup algebra K[S], where K is a field and S a semigroup, is formally defined in the same way as the group algebra K[G]. Similarly, a semigroup ring R[S] is a ...

A sheaf is a presheaf with "something" added allowing us to define things locally. This task is forbidden for presheaves in general. Specifically, a presheaf F on a ...