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A geodesic is a locally length-minimizing curve. Equivalently, it is a path that a particle which is not accelerating would follow. In the plane, the geodesics are straight ...

The first Göllnitz-Gordon identity states that the number of partitions of n in which the minimal difference between parts is at least 2, and at least 4 between even parts, ...

An algorithm for finding closed form hypergeometric identities. The algorithm treats sums whose successive terms have ratios which are rational functions. Not only does it ...

Gram-Schmidt orthogonalization, also called the Gram-Schmidt process, is a procedure which takes a nonorthogonal set of linearly independent functions and constructs an ...

A great circle is a section of a sphere that contains a diameter of the sphere (Kern and Bland 1948, p. 87). Sections of the sphere that do not contain a diameter are called ...

An elliptic partial differential equation given by del ^2psi+k^2psi=0, (1) where psi is a scalar function and del ^2 is the scalar Laplacian, or del ^2F+k^2F=0, (2) where F ...

There are at least two maps known as the Hénon map. The first is the two-dimensional dissipative quadratic map given by the coupled equations x_(n+1) = 1-alphax_n^2+y_n (1) ...

A second-order linear Hermitian operator is an operator L^~ that satisfies int_a^bv^_L^~udx=int_a^buL^~v^_dx. (1) where z^_ denotes a complex conjugate. As shown in ...

On a Riemannian manifold M, tangent vectors can be moved along a path by parallel transport, which preserves vector addition and scalar multiplication. So a closed loop at a ...

A hyper-Kähler manifold can be defined as a Riemannian manifold of dimension 4n with three covariantly constant orthogonal automorphisms I, J, K of the tangent bundle which ...