Sentence examples for basic result which from inspiring English sources

This section begins with a basic result, which plays a pivotal role in the forthcoming analysis.

Among others, the authors of [2] quote, in an equivalent form, the following basic result, which is certainly folklore.

We obtain a basic result which is used elsewhere in the text.

Now, we present some basic results which are necessary to prove the main results.

Section 2 introduces some basic results which are necessary for the proof of Theorem 1.1.

In this subsection, we produce several basic results which will be used in our later analysis.

In this section, we introduce preliminary facts and some basic results, which are used throughout this paper (refer to [9 15]).

In this section, we first recall some basic results, which will be used in the next section.

In this section, we introduce preliminary facts and some basic results, which are used throughout this paper [21, 22].

These results are consistent with nanoparticles previously synthesized by the coprecipitation of the Fe(II), Fe III), and Gd III) salts in the same basic solution, which did not result in a mixed oxide system, Gd2O3-Fe3O4, but a doped Gd:Fe3O4[55].

Now we give basic definitions and some basic results [6], which are helpful for improving our main results.