Numerical Computation of a Certain Dirichlet Series Attached to Siegel Modular Forms of Degree Two

The Rankin convolution type Dirichlet series D-F,D-G(s) of Siegel modular forms F and G of degree two, which was introduced by Kohnen and the second author, is computed numerically for various F and G. In particular, we prove that the series D-F,D-G(s), which shares the same functional equation and analytic behavior with the spinor L-functions of eigenforms of the same weight are not linear combinations of those. In order to conduct these experiments a numerical method to compute the Petersson scalar products of Jacobi Forms is developed and discussed in detail.

Effect Of Confined Impinging Jet Mixing Processing Parameters On Poly (Lactic Acid) Nanoparticle Morphology

Biodegradable nanoparticles are at the forefront of drug delivery research as they provide numerous advantages over traditional drug delivery methods. An important factor affecting the ability of nanoparticles to circulate within the blood stream and interact with cells is their morphology. In this study a novel processing method, confined impinging jet mixing, was used to form poly (lactic acid) nanoparticles through a solvent-diffusion process with Pluronic F-127 being used as a stabilizing agent. This study focused on the effects of Reynolds number (flow rate), surfactant presence in mixing, and polymer concentration on the morphology of poly (lactic acid) nanoparticles. In addition to looking at the parameters affecting poly (lactic acid) morphology, this study attempted to improve nanoparticle isolation and purification methods to increase nanoparticle yield and ensure specific morphologies were not being excluded during isolation and purification. The isolation and purification methods used in this study were centrifugation and a stir cell. This study successfully produced particles having pyramidal and cubic morphologies. Despite successful production of these morphologies the yield of non-spherical particles was very low, additionally great variability existed between redundant trails. Surfactant was determined to be very important for the stabilization of nanoparticles in solution but appears to be unnecessary for the formation of nanoparticles. Isolation and purification methods that produce a high yield of surfactant free particles have still not been perfected and additional testing will be necessary for improvement.¿

Detrital Zircon Evidence for Mixing of Mazatzal Province Age Detritus With Yavapai Age (ca. 1700-1740 Ma) and Older Detritus in the ca. 1650 Ma Mazatzal Province of Central New Mexico, USA

Preliminary detrital zircon age distributions from Mazatzal crustal province quartzite and schist exposed in the Manzano Mountains and Pedernal Hills of central New Mexico are consistent with a mixture of detritus from Mazatzal age (ca. 1650 Ma), Yavapai age (ca. 1720 Ma.), and older sources. A quartzite sample from the Blue Springs Formation in the Manzano Mountains yielding 67 concordant grain analyses shows two dominant age peaks of 1737 Ma and 1791 Ma with a minimum peak age of 1652 Ma. Quartzite and micaceous quartzite samples from near Pedernal Peak give unimodal peak ages of ca. 1695 Ma and 1738 Ma with minimum detrital zircon ages of ca. 1625 Ma and 1680 Ma, respectively. A schist sample from the southern exposures of the Pedernal Hills area gives a unimodal peak age of 1680 Ma with a minimum age of ca. 1635 Ma. Minor amounts of older detritus (>1800 Ma) possibly reflect Trans-Hudson, Wyoming, Mojave Province, and older Archean sources and aid in locating potential source terrains for these detrital zircon. The Blue Springs Formation metarhyolite from near the top of the Proterozoic section in the Manzano Mountains yields 71 concordant grains that show a preliminary U-Pb zircon crystallization age of 1621 ¿ 5 Ma, which provides a minimum age constraint for deposition in the Manzano Mountains. Normalized probability plots from this study are similar to previously reported age distributions in the Burro and San Andres Mountains in southern New Mexico and suggest that Yavapai Province age detritus was deposited and intermingled with Mazatzal Province age detritus across much of the Mazatzal crustal province in New Mexico. This data shows that the tectonic evolution of southwestern Laurentia is associated with multiple orogenic events. Regional metamorphism and deformation in the area must postdate the Mazatzal Orogeny and ca. 1610 Ma ¿ 1620 Ma rhyolite crystallization and is attributed to the Mesoproterozoic ca. 1400 ¿ 1480 Ma Picuris Orogeny.