Sentence examples for considered defined on from inspiring English sources
All the functions of A − will be considered defined on the same interval, suggested by the context.
For BVP (1.5), consider the functional defined on as follows: (2.3).
Consider the operator, defined on, as in the proof of Theorem 4.1.
Consider, defined as (1.46).
We suppose the random variables being considered are defined on a probability space ((Omega,mathcal {F},P)) for a base probability P. In order to explain comonotone additivity, we first note that two random variables X,Y are said to be comonotone if, for example, one is a monotone increasing function of the other.
In this sense, MC j1, j2) can be considered as defined on the range [ j1, j2].
Therefore we need to consider mappings defined on the subsets of R n which have nice properties with respect to a metric distance other than the regular norm.
Since we consider solutions defined on the whole real line, some special care is needed.
Three different settings are considered, with functions defined on the whole real line, a semi-axis and an interval, respectively, leading to different types of bounds.
where u ∗ = ( ξ 1 ∗, ξ 2 ∗, …, ξ n ∗ ) T. It is easy to verify that L − H T is the adjoint operator of L − H, while both are considered as operators defined on subspaces of [ L 2 ] n.
