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Another word for a C^infty (infinitely differentiable) manifold, also called a differentiable manifold. A smooth manifold is a topological manifold together with its ...

For d>=1, Omega an open subset of R^d, p in [1;+infty] and s in N, the Sobolev space W^(s,p)(R^d) is defined by W^(s,p)(Omega)={f in L^p(Omega): forall ...

The theory of analyzing a decision between a collection of alternatives made by a collection of n voters with separate opinions. Any choice for the entire group should ...

Given three mutually tangent circles, there exist exactly two nonintersecting circles which are tangent circles to all three original circles. These are called the inner and ...

A solvable Lie group is a Lie group G which is connected and whose Lie algebra g is a solvable Lie algebra. That is, the Lie algebra commutator series ...

Sorting is the rearrangement of numbers (or other orderable objects) in a list into their correct lexographic order. Alphabetization is therefore a form of sorting. Because ...

The number of regions into which space can be divided by n mutually intersecting spheres is N=1/3n(n^2-3n+8), giving 2, 4, 8, 16, 30, 52, 84, ... (OEIS A046127) for n=1, 2, ...

A sparse matrix is a matrix that allows special techniques to take advantage of the large number of "background" (commonly zero) elements. The number of zeros a matrix needs ...

Special affine curvature, also called as the equi-affine or affine curvature, is a type of curvature for a plane curve that remains unchanged under a special affine ...

The special unitary group SU_n(q) is the set of n×n unitary matrices with determinant +1 (having n^2-1 independent parameters). SU(2) is homeomorphic with the orthogonal ...