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The Church-Turing thesis (formerly commonly known simply as Church's thesis) says that any real-world computation can be translated into an equivalent computation involving a ...

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 ...

Let B_t={B_t(omega)/omega in Omega}, t>=0, be one-dimensional Brownian motion. Integration with respect to B_t was defined by Itô (1951). A basic result of the theory is that ...

The conjugate gradient method can be viewed as a special variant of the Lanczos method for positive definite symmetric systems. The minimal residual method and symmetric LQ ...

Transitivity is a result of the symmetry in the group. A group G is called transitive if its group action (understood to be a subgroup of a permutation group on a set Omega) ...

An initial point that provides safe convergence of Newton's method (Smale 1981; Petković et al. 1997, p. 1).

Barycentric coordinates (t_1,t_2,t_3) normalized so that they become the areas of the triangles PA_1A_2, PA_1A_3, and PA_2A_3, where P is the point whose coordinates have ...

A flow defined analogously to the axiom A diffeomorphism, except that instead of splitting the tangent bundle into two invariant sub-bundles, they are split into three (one ...

Axiomatic set theory is a version of set theory in which axioms are taken as uninterpreted rather than as formalizations of pre-existing truths.

The study of the nature and properties of bifurcations.