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A topological transformation in which a surface is made out of an infinitely elastic material which, however, may not be torn or cut. Using this simple prescription gives the ...

A projection is the transformation of points and lines in one plane onto another plane by connecting corresponding points on the two planes with parallel lines. This can be ...

A random permutation is a permutation containing a fixed number n of a random selection from a given set of elements. There are two main algorithms for constructing random ...

There are at least two theorems known as Salmon's theorem. This first states that if P and S are two points, PX and SY are the perpendiculars from P and S to the polars of S ...

The negative derivative S(v)=-D_(v)N (1) of the unit normal N vector field of a surface is called the shape operator (or Weingarten map or second fundamental tensor). The ...

A square matrix A is a special orthogonal matrix if AA^(T)=I, (1) where I is the identity matrix, and the determinant satisfies detA=1. (2) The first condition means that A ...

A square matrix U is a special unitary matrix if UU^*=I, (1) where I is the identity matrix and U^* is the conjugate transpose matrix, and the determinant is detU=1. (2) The ...

The first Strehl identity is the binomial sum identity sum_(k=0)^n(n; k)^3=sum_(k=0)^n(n; k)^2(2k; n), (Strehl 1993, 1994; Koepf 1998, p. 55), which are the so-called Franel ...

A second-order ordinary differential equation d/(dx)[p(x)(dy)/(dx)]+[lambdaw(x)-q(x)]y=0, where lambda is a constant and w(x) is a known function called either the density or ...

Toroidal functions are a class of functions also called ring functions that appear in systems having toroidal symmetry. Toroidal functions can be expressed in terms of the ...