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A condition in numerical equation solving which states that, given a space discretization, a time step bigger than some computable quantity should not be taken. The condition ...

In the calculus of variations, the condition f_(y^')(x,y,y^'(x_-))=f_(y^')(x,y,y^'(x_+)) must hold at a corner (x,y) of a minimizing arc E_(12).

A condition which must hold for a result to be true, but which does not guarantee it to be true. If a condition is both necessary and sufficient, then the result is said to ...

A necessary and sufficient condition for a sequence S_i to converge. The Cauchy criterion is satisfied when, for all epsilon>0, there is a fixed number N such that ...

Consider a function f(x) in one dimension. If f(x) has a relative extremum at x_0, then either f^'(x_0)=0 or f is not differentiable at x_0. Either the first or second ...

A set of residues {a_1,a_2,...,a_(k+1)} (mod n) such that every nonzero residue can be uniquely expressed in the form a_i-a_j. Examples include {1,2,4} (mod 7) and {1,2,5,7} ...

Eisenstein's irreducibility criterion is a sufficient condition assuring that an integer polynomial p(x) is irreducible in the polynomial ring Q[x]. The polynomial ...

A necessary and sufficient condition that there should exist at least one nondecreasing function alpha(t) such that mu_n=int_(-infty)^inftyt^ndalpha(t) for n=0, 1, 2, ..., ...

For real, nonnegative terms x_n and real p with 0<p<1, the expression lim_(k->infty)x_0+(x_1+(x_2+(...+(x_k)^p)^p)^p)^p converges iff (x_n)^(p^n) is bounded.

A necessary and sufficient condition for a measure which is quasi-invariant under a transformation to be equivalent to an invariant probability measure is that the ...