Sentence examples for the foregoing result from inspiring English sources
adjective
Occurring before or in front of something else, in time, place, rank or sequence.
The foregoing result is applicable for the case where the algebra interior of the system (3.1) is empty.
The foregoing result analysis indicates that the FDE algorithm can efficiently reduce unnecessary DE computation time while maintaining nearly similar coding efficiency as the original 3D-HEVC encoder.
Interchanging the roles of the operators (mathcal{G}_{1}) and (mathcal {G}_{2}) in the foregoing result, we can obtain a second result by requiring the condition: frac{ell}{kappaGamma(beta+1)} zeta-xi)^{beta} zeta-xi^{beta}bigl 1-e^{-kappa zeta instead of (2.5).
The foregoing results prompt us to investigate the synthetic potentiality of pyrazolone 1 toward a variety of electrophilic reagents.
Most recently, Alam et al. [16] extended the foregoing results for generalized φ-contractions due to Boyd and Wong [17].
Through the foregoing results, the mechanisms of substitution, as proposed in a previous work, have been confirmed to be independent of the type of solvent utilized.
From the foregoing results, quicklime is adjudged to have exhibited somewhat superior engineering properties and therefore creates a more effective stabilization alternative for the soil.
Thus, the foregoing results would be helpful for profoundly understanding the morphologic properties and functional foundation of both immature and mature BMDCs.
The foregoing results have great potential to be useful for further study in this area, such as linear neutral systems and nonlinear systems.
Although the site density is by no means perfect in many parts of the Central Andes, we believe that the foregoing results are a significant improvement over the older 2-D models.
However, a 2007 article surveyed these and other results, and concluded that "A conservative analysis of the foregoing results suggests that Vega is quite likely variable in the 1-2% range, with possible occasional excursions to as much as 4% from the mean".. Also, a 2011 article affirms on its abstract that "The long-term (year-to-year) variability of Vega was confirmed".
