For example, (({mathcal {O}}text {mathcal {F}})_{B}) for the odd degrees (l=1,3,5) increase in magnitude again from around 1980 to the end of the assimilation period.
For example ({mathcal N}_2={mathcal Z}{mathcal A}) and, more generally, ({mathcal N}_{c+1}={mathcal Z}{mathcal N}_c) for every (cge 1).
For example, when ({mathcal A}) is finite dimensional, then the two notions clearly coincide.
For example, though (({mathcal {O}}text {mathcal {F}})_{dot B}) decreases monotonically in time, the SV forecast is still very far away from the observations, as (({mathcal {O}}text {mathcal {F}})_{dot B} approx {mathcal {O}}(1)) for all degrees (see Fig. 4).
To be more precise, we give two examples for X such that ((mathcal M_{X}, d_{L})) is not separable: (i) Infinite unions of shrinking closed intervals with zero { 0 } cup bigcup_{n=1}^{infty}left[frac{1}{2^{n}}, frac{1}{2^{n}}+frac{1}{2^{n+1}}right]; (ii) Closed interval [0,1].
In what follows, we give an example for the case that (mathcal{H}) is finite dimensional.
For example, for domain (mathcal{D } = {mathsf{bob }, mathsf{paper }}), Fig. 2 depicts the Bayesian network over indicator variables of assertions (for the sake of space, names are abbreviated; for instance, (mathsf{hP }) denotes (mathsf{hasPublication };mathsf{b }) denotes (mathsf{bob }), and so on).
For example, for global coupling we have (mathcal{L}_{ij} = delta_{ij}-N^{-1}), and the ((N-1) degenerate) eigenvalue is +1.
For example for maximizing the total throughput, (mathcal {U} z)=z) can be used or for providing proportional fairness, (mathcal {U} z)=log (z)) can be considered [22, Chapter 5].
For example, the partitioning of ({mathcal {D}}({text{''Date"}})) can be by month or by season.
