Sentence examples for be the completion under from inspiring English sources
Let X and Y be the completion under ∥ ⋅ ∥ X and ∥ ⋅ ∥ Y, respectively.
Let be defined by (2.27) and be the completion of under the norm.
Let C 0 ∞ ( ℝ N ) denote the collection of smooth functions with compact support and D1,p ℝ N ) be the completion of C 0 ∞ ( ℝ N ) under | | u | | p = ∫ ℝ N | ∇ u | p d x.
Given a σ-field ({mathcal {G}}), the universal completion of ({mathcal {G}}) is the σ-field ({mathcal {G}}^{ast }=cap _{mathbb {P}} {mathcal {G}}^{mathbb {P}}), where ({mathbb {P}}) ranges over all probability measures on ({mathcal {G}}) and ({mathcal {G}}^{mathbb {P}}) is the completion of ({mathcal {G}}) under ({mathbb {P}}).
Overall, results revealed that most anaerobic treatment reactions were near completion under the previous treatment regime, that further Zn processing was likely practical, and a possible passive media regeneration technique, thus illuminating further options regarding high-strength acid mine drainage and raw municipal wastewater passive co-treatment.
Let be the Sobolev space of the completion of under the norm with the dual space, and denote the usual scalar product in.
The main difficulty for ones working on the vector setting is the non-completion of the order under consideration.
Agrawal (2009) conducted an economic analysis on five emerging shale gas plays in the United States for two types of completions vertical and horizontal to examine which completion method is the best under different economic environments.
The trial was registered after completion under Clinical Trials registration number ISRCTN31291803 (http://www.controlled-trials.com/ISRCTN31291803).
