In particular, our results extend some important inequalities in a classical situation; when (alpha=1 ), some relationships between these inequalities and the classical inequalities have been established.
Some classical inequalities are known also in a more general form of Banach lattice norms and/or in continuous forms (i.e., for 'continuous' many functions are involved instead of finite many as in the classical situation).
If there was something ambiguous or troubling, in the classical situation, about having to refer to subjective uncertainty over the location of the molecule while there is an objective fact on the matter, then it should be at least as troubling to have to refer to the statistical mixture of the demon's states when deciding to perform the resetting operation.
Definition 8 coincides with Definition 2 ofJarrow and Larsson (2012) for the classical situation in which a unique prior ({mathbb {Q}}) exists.
As far as the former is concerned, there is little difference from the classical situation: in SIA R is equipped with the usual addition and multiplication operations under which it is a field.
In contrast with the classical situation, the oscillations involve approximation of the identities or semigroups whose kernels decay fast enough and the resulting estimates take into account their lack of localization.
The validation of positive cases without validation of negative cases is a classical situation in such population surveillance systems.
This represents a classical situation of artificial over-inflation of zeros in count data analysis in the presence of relatively low counts and sample sizes.
In other words, the Wenzel model represents a classical situation of a droplet on a 'flat' surface just modified by a roughness factor.
The classical situation foresees the comparison of in vitro toxic concentrations with the known in vivo toxic doses, as major indication of biological relevance.
