A completely bounded bilinear operatorφ: M×M→M on a von Neumann algebra M is said to have a factorization in M if there exist completely bounded linear operatorsψj, θj: M→M such thatφ x, y)= ψj x) θj y), x, y∈M,where convergence of the sum is made precise below.
Literature survey also reveals that the N-acyl hydrazones synthesised from aromatic carbaldehyde are essentially planar and exist completely in the form of geometric (E -configuration about thE -configurationo steric hindrabouton the imine bond [10, 24–27].
Dr. Jeffery Ellenbogen 's research at Harvard indicates that if an incubation period includes sleep, people are 33percentt more likely to infer connections among distantly related ideas, and yet, as he puts it, these performance enhancements exist "completely beneath the radar screen".
"Water is a byproduct of the breakdown of carbohydrates, fats and proteins, and some birds can exist completely on that source alone" — though most do not.
What each of Tiree's tribes wants is an island just full enough of members of the same tribe, but where they can still exist completely without self-consciousness.
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The Dalai Lama asserted that morality can exist completely independently of religion, and that there are many secular people who are virtuous human beings, but that religion is an effective medium for promoting universally-positive, humanistic beliefs for those who are particularly receptive to faith.
"The hard part was finding the people who had the rights, literally looking for artists who had completely disappeared!" Such is the world of dance music that one-off club hits often exist completely independently from the artists behind them, who can continue in relative anonymity.
Here's a simple idea for the Palestinians in Gaza: Recognize Israel's right to exist and completely abandon the pursuit of its destruction.
Trying to get out of that and look at a future where I'm not constantly paying $1000 a month just to exist, is completely unrealistic for me right now.
