For a sequence of nondegenerate i.i.d. bounded random variables {Yn, n ≥ 1} defined on a probability space (Ω,F ,P) and a constant b > 1, it is shown for Wn = (b − 1) ∑n i=1 b Yi/b n+1 that S (FY1) ⊆ {c ∈ R : P ({ω ∈ Ω : c is a limit point of Wn(ω)}) = 1} = S (FV ) ⊆ [l, L] and that for almost every ω ∈ Ω, the set of limit points of Wn(ω) coincides with the set S (FV ) where S (FY1) and S (FV )...

A Mie backscattering model for spherical particles with off-center inclusion has been developed and tested. The program is capable of dealing with size parameter values up to approximately 1000, thus allowing one to simulate the optical behavior of a large variety of atmospheric aerosols, as well as cloud and precipitation particles. On the basis of this model, we simulated the optical properti...

Let C ⊆ P denote the rational normal curve of order d. Its homogeneous defining ideal IC ⊆ Q[a0, . . . , ad] admits an SL2-stable filtration J2 ⊆ J4 ⊆ · · · ⊆ IC by sub-ideals such that the saturation of each J2q equals IC . Hence, one can associate to d a sequence of integers (α1, α2, . . . ) which encodes the degrees in which the successive inclusions in this filtration become trivial. In thi...

Fig. 4. Age-related increase in number of inclusions in brains of male C57BL/6 mice. LBP-like immunoreactive clusters were quantified in 25-pim coronal sections through the dorsal hippocampus. For each animal, the number of clusters per unilateral hippocampus was determined in several sections and subsequently averaged. Numbers of mice were 6, 5, 4, 9, 9, and 17 at ages 0 to 2, 6, 9 to 10, 12 t...

and Applied Analysis 3 moreover we summarize some properties of a Hartman-type function. Lemma 4 (see [8]). LetG : I×I → R be the function defined as follows: as 0 ≤ t < η, G (t, τ) = { { { { { { { { { {

We compute the spectrum of the Neumann-Poincaré operator for two discs in R2. We show how the behavior of the eigenvalues relates to W 1,∞ estimates on the potential in 2D composites containing circular inclusions.

Microbialites can have complex morphologies that preserve clues to ancient microbial ecology. However, extracting and interpreting these clues is challenging due to both the complexity of microbial structures and the difficulties of connecting morphology to microbial processes. Fenestrate microbialites from the 2521±3 Ma Gamohaan Formation, South Africa, have intricate structures composed of th...

Plate tectonics and volcanism involve the formation, migration, and interaction of magma and gas. Experiments show that melt inclusions subjected to a thermal gradient migrate through olivine crystals, under the kinetic control of crystal-melt interface mechanisms. Exsolved gas bubbles remain fixed and eventually separate from the melt. Scaled to thermal gradients in Earth's mantle and geologic...