Sentence examples for follows throughout from inspiring English sources

In what follows throughout this section, we assume the following: X is a smooth, strictly convex, and reflexive Banach space; C is a nonempty closed convex subset of X. X is a smooth, strictly convex, and reflexive Banach space; C is a nonempty closed convex subset of X.

Therefore, the UE traffic pattern can be formulated as a non-linear programing problem [17, 18] as follows (throughout the manuscript, all terms are non-negative unless otherwise stated): [UE-TAP]: begin{aligned} &{hbox{min} }, {z(x) = sumlimits_{a in A} {int_{0}^{{x_{a} }} {t_{a} (x_{a} + bar{x}_{a} ),{text{d}}x} } } & s.t.

Along with a brief introduction about the study, the definition of product reuse and recycling was provided as follows: Throughout this survey, product "reuse" refers to the return to use of complete products when possible and "recycling" refers to the processing of differentiating collection and refusing disposal of consumable items for recovery of materials or energy.

The author has plot devices that he follows throughout his Goosebumps books.

Following one another's leads, some demanding silence and others attaching themselves to what came before them, there is a charming awkwardness that follows throughout.

The chord progression F-E♭-Dm-Dm-E♭-F follows throughout her edition while the middle eight remains in F (Pallot's version did not contain a middle eight).

More searches followed throughout the next year.

Similar death and change followed throughout the Southeast.

Interdisciplinary and cross-linguistic approaches are followed throughout.

"Flacco is closely followed throughout Delaware and the region.

This trial is highly sensitive and is followed throughout the world.