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Elliptic curve primality proving, abbreviated ECPP, is class of algorithms that provide certificates of primality using sophisticated results from the theory of elliptic ...

A submersion is a smooth map f:M->N when dimM>=dimN, given that the differential, or Jacobian, is surjective at every x in M. The basic example of a submersion is the ...

The Jacobian of the derivatives partialf/partialx_1, partialf/partialx_2, ..., partialf/partialx_n of a function f(x_1,x_2,...,x_n) with respect to x_1, x_2, ..., x_n is ...

Levenberg-Marquardt is a popular alternative to the Gauss-Newton method of finding the minimum of a function F(x) that is a sum of squares of nonlinear functions, ...

Let a be the angle between v and x, b the angle between v and y, and c the angle between v and z. Then the direction cosines are equivalent to the (x,y,z) coordinates of a ...

The canonical bundle is a holomorphic line bundle on a complex manifold which is determined by its complex structure. On a coordinate chart (z_1,...z_n), it is spanned by the ...

States that for a nondissipative Hamiltonian system, phase space density (the area between phase space contours) is constant. This requires that, given a small time increment ...

A map defined by one or more polynomials. Given a field K, a polynomial map is a map f:K^n->K^m such that for all points (x_1,...,x_n) in K^n, ...

The tangent plane to a surface at a point p is the tangent space at p (after translating to the origin). The elements of the tangent space are called tangent vectors, and ...

For omega a differential (k-1)-form with compact support on an oriented k-dimensional manifold with boundary M, int_Mdomega=int_(partialM)omega, (1) where domega is the ...