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The distinct texture changes taking place in each alloy are interpreted in terms of differences in the strengths and distributions of the initial texture components.
With this conceptualization, the distributions of the initial dissolution rate coefficient and the sorption/desorption rate coefficient are represented as probability density functions.
(10) and (15) are different, meaning that estimations of the piezomagnetic field differ according to the assumed distributions of the initial magnetizations: an assumption of uniform direction yields Eq. (10), while an assumption of minimum magnetizations yields Eq. (15).
In the case that the direction of the initial magnetizations is assumed to be uniform, the piezomag-netic field is uniquely determined from the initial magnetic anomalies, regardless of the non-uniqueness of the explicit distributions of the initial magnetizations.
It turns out that, in spite that for fixed h every Wigner distribution satisfies a Liouville equation, their limits are no longer uniquely determined by those of the Wigner distributions of the initial data.
The molecular weight distributions of the initial fractions separated were much narrower compared with those obtained by using silica gels, as CPG has a narrower distribution in the pore size.
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We assume that the initial state x0 is distributed according to a density function f x0), and that h z0|x0) is the distribution of the initial observation.
The initial states x0 and s0 are distributed according to a density function f x0); initial observation h (z0|x0) is the distribution of the initial observation.
The particle size distribution of the initial powder ranged from 1 to 100 um.
(c) Distribution of the initial sea-surface height estimated by tsunami-waveform inversion.
Priori distribution of the initial state x0 is assumed to be p x0).
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