Sentence examples for and define the set from inspiring English sources

For the sequence spaces and, define the set by (2.4).

We can go further and define the set N of natural numbers.

(1.6) Let B be a maximal monotone operator on H and define the set of zero points of B as follows: B^{-1}0={xin H: 0in Bx}.

Let ε > 0 and define the set S = { k r ∈ N : 1 k r ∑ k = 1 k r | x k y k − L | p k < ε }.

Let us consider an unknown parameter vector x ∈ R n and define the set of the possible values of x as X ≜ { possible values of x } ⊆ R n. Suppose we aim at estimating x from a random vector.

Let us reconsider system (3.11) and define the set K= bigl{ u in X: bigllangle v,u(t) bigrrangle geq t 1-t)|u|_{v} mbox{ for } t 1-t,1] bigr}.

Let and be nonnegative continuous concave functionals on, and let and be nonnegative continuous convex functionals on ; then for positive numbers and, define the sets.

The elimination of the logic quantifier produces a boolean function which is free of the quantified variable, and defines the set of design parameters that satisfy the design specifications.

Brick, polished wood and glass define the setting.

For nonnegative numbers and define the following convex sets: (2.3).

Let and define the sequence by setting for Let Then (3.2). so by hypothesis is compact.