Sentence examples for intervals discussed from inspiring English sources

Secondly, this paper generalizes the boundary value problems on finite intervals discussed in [12, 13] to ones on the whole lines, the main tools used in this paper is the well-known Schauder fixed point theorem (not the upper and lower solution method, the fundamental properties of the fixed point index, and the fixed point index theorem used in [12, 13]).

Average grain aspect ratio, average grain circularity, and average grain roundness are in the range 1.54 1.76, 0.69 0.79, and 0.61 0.73, respectively (Table 1). Figure 6 shows the grain size distribution for each of the sampled intervals (discussed in detail below).

The Bayesian framework offers an alternative approach to the Frequentist significance levels and confidence intervals discussed in the previous section.

To investigate the generality of this finding, spectra were calculated for all of the intervals discussed above.

Notably, 7 of these positions were located in the epitope regions and nearly all the mutations in these positions mapped to the putative positive selection intervals discussed above (the green intervals in Figures 3 and 4).

Fourthly, we generalize the boundary value problems of differential equations on finite interval discussed in [12, 13] to one in whole lines.

This figure also includes the number of significant changes in gene expression observed in each interval, discussed above.

The one that started the match like greased lightning or the one that trooped off at the interval discussing what had gone wrong?

Possible mechanisms of solar climatic connections, which may be of importance over short and long time intervals, are discussed.

The construction of confidence intervals is discussed and a proposition is made to account for the skewness of the sampling distribution of the QSR.

The main emerging themes within the appraisal and help-seeking intervals are discussed below.