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Two families of equations used to find roots of nonlinear functions of a single variable. The "B" family is more robust and can be used in the neighborhood of degenerate ...

A class of subvarieties of the Grassmannian G(n,m,K). Given m integers 1<=a_1<...<a_m<=n, the Schubert variety Omega(a_1,...,a_m) is the set of points of G(n,m,K) ...

The p×p square matrix formed by setting s_(ij)=xi^(ij), where xi is a pth root of unity. The Schur matrix has a particularly simple determinant given by ...

A function f in C^infty(R^n) is called a Schwartz function if it goes to zero as |x|->infty faster than any inverse power of x, as do all its derivatives. That is, a function ...

A conformal mapping from the upper half-plane to a polygon.

Let f be analytic on the unit disk, and assume that 1. |f(z)|<=1 for all z, and 2. f(a)=b for some a,b in D(0,1), the unit disk. Then |f^'(a)|<=(1-|b|^2)/(1-|a|^2). (1) ...

The Schwarz triangles are spherical triangles which, by repeated reflection in their indices, lead to a set of congruent spherical triangles covering the sphere a finite ...

A periodic minimal surface constructed by Schwarz using the following two principles: 1. If part of the boundary of a minimal surface is a straight line, then the reflection ...

A polyhedron constructed by ruling 2n equally spaced vertical lines along the surface of a cylinder together with 2n^3 circles around the cylinder at equally spaced heights. ...

If we expand the determinant of a matrix A using determinant expansion by minors, first in terms of the minors of order r formed from any r rows, with their complementaries, ...