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Let each sphere in a sphere packing expand uniformly until it touches its neighbors on flat faces. Call the resulting polyhedron the local cell. Then the local density is ...

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, ...

A p-form alpha is indecomposable if it cannot be written as the wedge product of one-forms alpha=beta_1 ^ ... ^ beta_p. A p-form that can be written as such a product is ...

A system of variables which can be written in the form of Hamilton's equations.

A real-linear vector space H equipped with a symplectic form s.

A transformation of the form A^'=UAU^(H), where U^(H) denotes the conjugate transpose.

Erdős proved that there exist at least one prime of the form 4k+1 and at least one prime of the form 4k+3 between n and 2n for all n>6.

A second-order ordinary differential equation of the form

An ordinary differential equation of order n is an equation of the form F(x,y,y^',...,y^((n)))=0.

For every even dimension 2n, the symplectic group Sp(2n) is the group of 2n×2n matrices which preserve a nondegenerate antisymmetric bilinear form omega, i.e., a symplectic ...