In Kupper and Schachermayer (2009), the authors showed that every dynamic LM-measure, which is finite, normalized, strictly monotone, continuous, law invariant, admits The Fatou property, and is strongly time consistent, can be represented as (48) for some U.
In Appendix B, we prove that the normalized cut strictly increases when one community is split into two.
If E is uniformly smooth, then J is uniformly norm-to-norm continuous on each bounded subset of E. If E is reflexive smooth and strictly convex, then the normalized duality mapping J is single-valued, one-to-one and onto.
TGN retrieval ratios were normalized and strictly standardized mean difference (SSMD) values were calculated, both for the normalized TGN retrieval ratio and for the cellular anti-CD8 intensity, to allow hit selection based on a statistical analysis (see Experimental Procedures).
The system becomes strictly priority driven when the normalized average system delay is high, i.e., high system delay reduces the channel awareness of the scheduler: highest priority packets are assigned resources with reduced importance of channel quality in the scheduling decisions.
On the other hand, the PPS scheduling function becomes strictly priority aware only under higher normalized system delay.
We note that if E is smooth, strictly convex, and reflexive, then the normalized duality mapping J is single-valued, one-to-one, and onto.
If E is a smooth, reflective and strictly convex Banach space, then the normalized duality mapping J : E → 2 E ∗ is single-valued, one-to-one and surjective.
We know that if E is uniformly smooth, strictly convex, and reflexive, then the normalized duality mapping J is single-valued, one-to-one, onto and uniformly norm-to-norm continuous on each bounded subset of E.
(iii) If E is a smooth, reflective and strictly convex Banach space, then the normalized duality mapping J : E → 2 E ∗ is single-valued, one-to-one and surjective.
