Sentence examples for using several results of from inspiring English sources

The q-analogues of many well known formulas are derived by using several results of q-Bernoulli, q-Euler numbers and polynomials.

In this article, we derive q-analogues of many well known formulas by using several results of q-Bernoulli, q-Euler numbers, and polynomials.

Then, assuming the existence of fixed points for maps in our classes of operators and using several results of Alber and Guerre-Delabriere [7], we prove convergence theorems with estimates of the convergence rates.

Case studies are presented to illustrate the feasibility of the approach, and the model was tested using several examples, the results of which are consistent with existing data in the literature.

The paper discusses the process of refinement of the collected data and statistical evaluation of results using several rounds of data collection from experts.

The fractions given below for colonies with the indicated features are based on results using several vectors of the same general structure as those shown in Figure 1.

Transformation of crystallographic plane of the commercial powder Si (400) to the NPS {(111), (220), (211), (312) and (400)} is resulted, using several concentrations of (KOH) as the etchant and wetting agent {n-propanol (NPA)}.

This section gives some lemmas that will be used to prove several results of this paper.

In order to find a variety of results, try using several of them for each search, such as Torch (http://xmh57jrzrnw6insl.onion/) and TorSearch (http://kbhpodhnfxl3clb4.onion/).

Simulation results have been obtained using several images but the results of "Biltmore Estate" image are presented in Figures 3(a)–3(f).

We derive a general approximation method that allows us to calculate the attractor of time-periodic landscapes, and demonstrate using several examples that the results of the approximation and the limiting cases of very slow and very fast changes are in perfect agreement.