Sentence examples for well defined from from inspiring English sources

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.

Since the Caratheodory function satisfies (CAR), the Nemytskii operator generated by,, is well defined from into, continuous, and bounded ([3, Proposition ]).

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.

Therefore the Leray-Schauder degree is well defined for, and from the homotopy invariant property of that degree we have (4.13).

which together with hypothesis (20), implies that Thus we have proved that (3.7) has no solution on then we get that for each, the Leray-Schauder degree is well defined for, and from the properties of that degree, we have (3..12).

The structure of the GAAA tetraloop receptor interaction is well defined solely from experimental NMR data, shows minor deviations from previously solved crystal structures, and verifies the previously inferred hydrogen bonding patterns within this motif.

Neither peak is particularly well defined, judging from the resolution curve and analysis of the confidence ranges.

DQA1∗01 04:02 was not common and well defined, differing from DQA1∗01 04:01 at position 5433 A→C in exon 3 leading to a synonymous base substitution.