Sentence examples for a sequence of assumptions from inspiring English sources

We state a sequence of assumptions on the random graph ensemble needed to establish our main result.

In a sequence of frames, the typical assumption (usually true) is that a site is not corrupted at the same location in consecutive frames.

In our case, we have X 0 R ( t ), X 1 R ( t ), X 2 R ( t ), …, X M - 1 R ( t ) is a sequence of independent random variables (Assumption 1).

Our study of the stability properties for the perturbed (VVI) problem with a sequence of converging mappings is under appropriate assumptions on the function defining the (VVI) problem rather than on the (VVI) problem as a whole.

If ({X_{i}, ige 1}) is a sequence of NA random variables satisfying the assumptions of Theorem 2.2, then from the maximal inequality of NA random variables (see [8, Theorem 2]), the condition (2.4) can be weakened by (2.1).

Remark 3.2 It is interesting that the assumption on a sequence of scalars { β n } is a very mild condition.

By virtue of a sequence of gap functions and a key assumption, Painleve-Kuratowski lower convergence of the solution sets is established.

Under suitable assumptions, we obtain a sequence of solutions associated with a sequence of positive energies going toward infinity.

Moreover, from assumption, there exists a sequence of elements such that.

Under the assumption that is a sequence of independent identically distributed random variables, many limiting results have been obtained.

To obtain Painleve-Kuratowski lower convergence of the solution sets, we introduce a sequence of gap functions based on the nonlinear scalarization function introduced by Chen et al. in [14] and a key assumption imposed on the sequence of gap functions.