Sentence examples for continuous by using from inspiring English sources

It is easy to prove that the mappings are completely continuous by using Arzelà-Ascoli theorem.

Consequently, is completely continuous by using the Arzela-Ascoli theorem [3].

Proof Noticing that f : [ 0, 1 ] × R n → R is continuous, by using the Ascoli-Arzela theorem and standard arguments, the result can easily be shown.

Very recently, Zhu et al.[26] obtain the existence results when a nonlocal item g is Lipschitz continuous by using the Hausdorff measure of noncompactness and operator transformation.

Thus (widetilde{T}: X rightarrow X) is completely continuous, by using the Schauder fixed point theorem, T̃ has at least a fixed point ((u^, v^ )) such that ((u^, v^ )=widetilde{T} u^, v^)).

Remark 1 If f ( t, u 1, u 2 ) : [ 0, 1 ] × [ 0, ∞ ) × → [ 0, ∞ ) is continuous, we can obtain that A : P 1 → P 1 is completely continuous by using a similar argument as the above. In this section, we discuss the existence of single or twin positive solutions to problem (2).

Spike detection and sorting was applied to the continuous recordings by using the well-established "wave-clus" software75.

Here, the slip ratio is approximated to a continuous function by using a sigmoid function.

Thus, methods generating such spatially continuous data by using point samples become essential tools.

The elastic stop is modelled in a continuous way by using the contact law of Hertz.

This paper presents an approach for learning grasping with continuous servoing by using large-scale data collection on a cluster of up to 14 individual robots.