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A principal nth root omega of unity is a root satisfying the equations omega^n=1 and sum_(i=0)^(n-1)omega^(ij)=0 for j=1, 2, ..., n. Therefore, every primitive root of unity ...

The path traced out by a fixed point at a radius b>a, where a is the radius of a rolling circle, also sometimes called an extended cycloid. The prolate cycloid contains ...

A quintic surface is an algebraic surface of degree 5. Togliatti (1940, 1949) showed that quintic surfaces having 31 ordinary double points exist, although he did not ...

Let C be a curve and let O be a fixed point. Let P be on C and let Q be the curvature center at P. Let P_1 be the point with P_1O a line segment parallel and of equal length ...

A radial function is a function phi:R^+->R satisfying phi(x,c)=phi(|x-c|) for points c in some subset Xi subset R^n. Here, |·| denotes the standard Euclidean norm in R^n and ...

A quotient of two polynomials P(z) and Q(z), R(z)=(P(z))/(Q(z)), is called a rational function, or sometimes a rational polynomial function. More generally, if P and Q are ...

The Rayleigh functions sigma_n(nu) for n=1, 2, ..., are defined as sigma_n(nu)=sum_(k=1)^inftyj_(nu,k)^(-2n), where +/-j_(nu,k) are the zeros of the Bessel function of the ...

Relaxation methods are methods of solving partial differential equations that involve splitting the sparse matrix that arises from finite differencing then iterating until a ...

Resolution is a widely used word with many different meanings. It can refer to resolution of equations, resolution of singularities (in algebraic geometry), resolution of ...

The consideration of the result of a numerical calculation as a function of an adjustable parameter (usually the step size). The function can then be fitted and evaluated at ...