Sentence examples for meant a function from inspiring English sources

By a solution of the system (3.1), we meant a function u ≡ u x, t) defined on ℝ × I, where I: = [0, T], satisfying the following conditions: (a) u, u t, u x, u xx ∈ C(ℝ × I).

By this is meant a function f that takes us from a pair ⟨p,q⟩ of sentences to a set f ⟨p,q⟩) of pairs of alternatives (perhaps possible worlds).

By a double sequence in E is meant a function f : N × N → E defined by f ( n, m ) = x n, m ∈ E. A double sequence { x n, m } is said to converge strongly to x ∗ if given any ϵ > 0, there exist N, M > 0 such that ∥ x n, m − x ∗ ∥ < ϵ for all n ≥ N, m ≥ M. If ∀ n, r ≥ N, ∀ m, t ≥ M, we have ∥ x n, r − x m, t ∥ < ϵ, then the double sequence is said to be Cauchy.

By a quasipseudometric on a set, we mean a function such that for all, (i), (ii).

By a solution of (1.1) we mean a function (xin PC^{2}(mathbb{R})) satisfying (1.1).

By a solution of (1.1) we mean a function in satisfying the relations in (1.1).

By a proper solution of (1.6) on we mean a function which has a property that and satisfies (1.6) on.

By a solution of (1.3), we mean a function such that and (1.3) is satisfied on identically.

By a solution of problem (1.10), (7), (8) we mean a function such that there exists a function with for each and (1.3), (1.4), (1.5) hold.

where is a positive constant which will be chosen later and denotes the usual norm in that is, Namely, by a solution to (2.10), we mean a function.

By a solution of (4.5 - 4.6), and for continuous controls we mean a function satisfying (4.5) for every and the impulses (4.6).