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By Sankey J

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Extra resources for Vertebrate paleontology and magnetostratigraphy of the upper Aguja Formation (late Campanian), Talley Mountain Area, Big Bend National Park, Tex

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G. 16) is N (N ) dEt = j=1 N (j) 1 (j) (j) (j) idϕt − dϕt 2 exp iϕt . 19) consists of a sum of independent randomly phased Wiener processes, with variance equal to BN dt, while the second term is independent of the scatterer label j. 20) where ξt is a complex Wiener process satisfying |dξt |2 = dt, dξt2 = 0. The process ξt is adapted to the filtration F (ϕ) = j F (j) , where F (j) is the filtration (j) appropriate to the component scatterer phase ϕt . 21) where the continuous valued random variable x, the average scattering ‘power’, ¯ .

It follows that the current vanishes, and thus detailed balance is equivalent to equilibrium. The corresponding situation in higher dimensions is more subtle – we develop this below. e. it has vanishing divergence. In accordance with a basic theorem from vector calculus, it can therefore be expressed in terms of a vector potential A as P v = ∇×A which in our case shall be interpreted in terms of the embedding of v (an inherently two-dimensional vector) into Euclidean 3-space, and the potential A necessarily exists in the three-dimensional space.

A measure of the size of this population (in the continuum limit) is what is referred to as the scattering cross-section and its statistical characteristics are independent of those of any external electromagnetic radiation that might be used to indirectly probe the properties of the population. From an experimental point of view, the crosssection is usually the object of primary interest and various experiments are designed to infer its behaviour from the properties of electromagnetic radiation that scatters from or propagates through the random medium.

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