Sentence examples for for our proof from inspiring English sources

The key ingredient for our proof is a tile decomposition of the operator supj|Snj f)| which depends on both the function f and on the lacunary structure of the frequencies.

The following existence theorem of an asymptotically nonexpansive mapping is useful tools for our proof.

In Section 2, we give some preliminary lemmas which are key tools for our proof.

The properties of P on D k and G j are important for our proof.

All source code and configuration instructions for our proof of concept are available from [36].

In Section 2, we give some definitions and preliminary lemmas which are key tools for our proof.

Here, we theoretically indicated that the electronic conduction efficiency of the sulfur host nanomaterial plays a crucial role in determining the sulfur content, and a highly efficient single-wall carbon nanotube (SWCNT) conductive network was constructed for our proof-of-concept studies, resulting in an unprecedentedly high sulfur content up to 95 wt%.

For our proof-of-concept scenario, we focus on the STP mode.

For our proof-of-concept work [32], we modified the above two equations slightly in order to use integer operations for the mean and covariance matrix computations.

The following lemma and results are useful for our proofs.

Before going to our main section, we first introduce some necessary lemmas which are crucial for our proofs.