Sentence examples for provides the sufficient from inspiring English sources

The following theorem provides the sufficient condition for the existence of positive definite solutions of (1.1).

To estimate the β's, the fitting process provides the sufficient data by regression tools [33, 34].

But he supposed in all such cases there is some unconscious perception or passion that provides the sufficient reason).

Lemma 1 provides the sufficient condition for a CSMA/CA-based scheduling framework to achieve throughput optimality.

Note that Proposition 4 only provides the sufficient conditions for when the educational stock increases and when it falls with more harsh punishment of the informal sector without considering the financing of the reform.

The template-aided preparation of G/PANI nanocomposites was aimed at reducing the aggregation of the nanocomposites, which improves the electrical conductivity and provides the sufficient electrolyte accessibility to the electrode/electrolyte interface.

In other words, the ISM band may not provide the sufficient number of interference-free channels.

Remark 3.3 Let us provide the sufficient condition of the boundedness of { A x n }.

These parsing and labeling configurations provide the sufficient conditions for the following energy-scalable algorithms.

Before deciding to invest in the petroleum project, the engineers will describe this project by providing the sufficient economic data.

Moreover, we provide the sufficient conditions for extinction, nonpersistence in the mean and weak persistence of this models.