Sentence examples for provided the existence from inspiring English sources

Fourier-transform infrared spectroscopic and X-ray photoelectron spectroscopic studies provided the existence of interactions in the PMVT blends and complexes.

In this manuscript, based on a fixed point theorem, we provided the existence result for a fractional finite difference inclusion in the presence of the general boundary conditions.

Furthermore, we willdenoted the complexity class of f by Θ ( l ) provided the existence of a function l ∈ RT such that f ∈ Ω l l ) ∩ O ( l ).

Choudhury [16] further extended the result of [25] and provided the existence results of coupled coincidence points for compatible mappings in partially ordered fuzzy metric spaces.

Requirement (i), for example, is met because primitive reconfigurations are atomic low-level operations amenable to be rolled-back, provided the existence of associated reconfiguration monitoring mechanisms.

That is, in these works the authors study questions related to stationary points of nonexpansive multivalued mappings provided the existence of approximate stationary point sequences is guaranteed.

Theorem 3.8 provides the existence of the solution u ∈ C ∞.

We provide the existence of a positive solution for the quasilinear elliptic equation.

Consequently, Theorem 2.3 provides the existence and uniqueness of the fixed point of f. □.

In Section 1, we provide the existence and nonexistence of solutions of system (1).

Our main result provides the existence of a (positive) solution for problem (P).