Then there exists a Hölder continuous representative of the L 2 -class of ν on B ¯ R + ( x 0 ), and for this representative ν ¯, | ν ¯ ( x ) − ν ¯ ( z ) | ≤ C κ ( | x − z | R ) α (2.9).
Then there exists a Hölder continuous representative of the L 2 -class of ν on B ¯ R + ( x 0 ), and for this representative ν ¯ we have | ν ¯ ( x ) − ν ¯ ( z ) | ≤ C κ ( | x − z | R ) α (2.9).
Then there exists a Hölder continuous representatives of the L2-class of ν on B ̄ R + ( x 0 ), and for this representative v ̄ there holds: | v ̄ ( x ) - v ̄ ( z ) | ≤ C κ | x - z | R α, (2.9).
The I.N.S. policy does take some account of the possibility of government coercion: where special circumstances -- such as definite coercion directed at an individual parent -- exist, a nonparental representative may be necessary to speak for the child.
The main motivation behind these approaches is that while the expression levels of thousands of genes have been measured, there exists a smaller subset which is representative of the underlying phenomenon being investigated.
This means that, for any given test sample and analyte, there exists a minimum test portion size that achieves a truly representative sample.
Many methods exist for selecting a representative topology for a set of unrooted trees, few exist for assigning branch lengths to a fixed topology, and even fewer for simultaneously setting the topology and branch lengths.
On the other hand, in opposition to this Christian tradition, there existed a sceptical tradition of which the greatest representative was Thomas Hobbes.
Whilst Indigenous Australians experience poorer health than other Australians, there exists little representative data to outline the burden and consequences of mental illness.
"I think the oversight up to 2007 was abysmal: it just didn't exist," said Representative Bill Delahunt, a Massachusetts Democrat who has organized a series of recent hearings, including the one with Mr. Bellinger.
