By the definitions of Φ, Ψ, J, we know that Ψ' is compact, Φ is weakly lower semi-continuous and bounded on each bounded subset of X. From lemma 1 we can see that -1 is well defined, from condition (G), J is well defined and continuously Gâteaux differentiable on X, with compact derivative.
Episodic migraine was well defined from the beginning of these classifications and after Galen, was named Hemicrania.
This solution is obtained in the Hardy class, for which the natural free energy is well defined from the initial time.
It is well defined from the Table 5 and so is shown in Fig. 3a and b, that Temkin isotherm data fitted quite well.
It was observed that the peak splitting is well defined from 20 mK up to 1.2 K and beyond this temperature the peak splitting smeared out.
However, while it is an extremely powerful exploratory data analysis tool, and is well defined from the information theory perspective, PCA-derived components lack physical constraints.
Since the Caratheodory function satisfies (CAR), the Nemytskii operator generated by,, is well defined from into, continuous, and bounded ([3, Proposition ]).
For a single event, the location depends on storm magnitude which cannot be well defined from the data sets, creating a spread of data with an envelope curve defined for the largest events.
Define a continuous function f from C into [ 0, ∞ ) by f ( x ) = lim sup n → ∞ η ( ∥ T n u − x ∥ ) (9). for all x ∈ C. Then f is well defined from the assumption.
It follows from assumption (f1) that the Nemytskii operator (N_{f}) generated by f, ((N_{f}u)(x)=f x,u(x))), is well defined from Y into (Y^), continuous, and bounded (see for example [32]).
