Sentence examples for aforesaid result from inspiring English sources

In order to introduce the aforesaid result we need to fix a few pertinent notions.

In the latter section, we discuss the feasibility of using the Matthews fixed point theorem as a mathematical tool for the asymptotic complexity analysis of algorithms and, in particular, we show that the aforesaid result is not, in principle, appropriate for such a purpose.

It is worth to mention that the aforesaid results were published for the first time in [17].

The aforesaid results are also coherent with our previous study of nonstoichiometric Hf-silicate materials in which we have evidenced the formation of HfO2 and SiO2 phases as well as Si nanoclusters (Si-ncs) upon annealing treatment [14, 22].

In order to provide the aforesaid results we introduce a new notion of completeness, which entails the order and the topology at the same time, and an appropriate notion of order-continuity.

We introduce the notions of a weakly contractive mapping and a weakly Kannan mapping in the partial metric framework, and we present a partial metric version of Theorems 9 and 10 in such a way that both aforesaid results are retrieved as a particular case when the partial metric is, in fact, a metric.

From these aforesaid results it can be concluded that Resveratrol influences the two kinases namely GSK3β and ERK1/2 (Fig. 6).

We have observed the relative values of the components of the flux vector v that are involved in the aforesaid resulting pathway.

The second, independent method (CervistaTM) confirmed the aforesaid results with 100% concordance with the exception of three cases which had low genomic DNA for which it was not possible to perform the test.

However, in the aforesaid reference it was shown that, at first, such ananalysis cannot be carried out through the aforementioned result.

In spite of the aforesaid limitations, results from the present study contribute to its accruing evidence-base.