Sentence examples for both aforesaid from inspiring English sources

Typical examples of algorithms whose running time of computing can be obtained by means of the recurrence (1) are Quicksort (best case behavior) and Mergesort (all behaviors) (see [45] for a detailed discussion about the both aforesaid algorithms).

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.

It is important to note that, for very wide spectra, the three-step solution could inspire a new method for spectral analysis in which separating the waveform into low- and high-frequency components could result in the rapid and accurate detection of the spectral components of both the aforesaid bands by adapting the duration of the analysis window to the lowest frequency of each band.

In this paper, we successfully applied the aforesaid parameters both in an Ordovician carbonate reservoir of the Tuoputai region of the Tarim Basin (NW China), and in an Eocene clastic lacustrine reservoir of the Fushan Depression in the Beibuwan Basin, South China Sea.

Whilst Conchobar was an unremitting opponent of Muirchertach Ua Briain; Donnchad was married to Domnall mac Taidc's sister, and possessed a claim of his own to the kingship Dublin, as both his father and grandfather the aforesaid Murchad and Diarmait mac Maíl na mBó had held it during their careers.

This test was more sensitive than both VI and IFAT and can replace the aforesaid methods for virus detection during outbreaks of BRD.

For the two aforesaid models, we plot, in Fig. 5, both the American and European option values as a function of their moneyness.

It is worth to observe that the aforesaid window function is very important both in terms of analysis resolution and of spectral leakage.

Tsunami signals show significant larger spectral energy levels at the aforesaid periods than the background signals at both stations.

The aforesaid polarization studies showed that in our case, both the former and latter take place.

Granted to the implementation a friendly-to-use front-end interface, the user is allowed to define a starting configuration of elements (subcellular vehicles, antimicrobials and other substances) inhabiting the aforesaid membranes, specifications and rules according to which both elements and membranes evolve through a number of iterations.