INTERPOLATING BLASCHKE PRODUCTS AND ANGULAR DERIVATIVES

We show that to each inner function, there corresponds at least one interpolating Blaschke product whose angular derivatives have precisely the same behavior as the given inner function. We characterize the Blaschke products invertible in the closed algebra H-infinity[(b) over bar : b has finite angular derivative everywhere. We study the most well-known example of a Blaschke product with infinite angular derivative everywhere and show that it is an interpolating Blaschke product. We conclude the paper with a method for constructing thin Blaschke products with infinite angular derivative everywhere.

Interpolating Blaschke Products and Angular Derivatives

We show that to each inner function, there corresponds at least one interpolating Blaschke product whose angular derivatives have precisely the same behavior as the given inner function. We characterize the Blaschke products invertible in the closed algebra generated by the algebra of bounded analytic functions and the conjugates of Blaschke products with angular derivative finite everywhere. We study the most well-known example of a Blaschke product with infinite angular derivative everywhere and show that it is an interpolating Blaschke product. We conclude the paper with a method for constructing thin Blaschke products with infinite angular derivative everywhere.

Vibrational spectroscopic monitoring of CO2-O energy transfer: cooling processes in atmospheres of Venus & Mars

The vibrational excitation of CO2 by a fast-moving O atom followed by infrared emission from the vibrationally excited CO2 has been shown to be an important cooling mechanism in the upper atmospheresof Venus, Earth and Mars. We are trying to determine more precisely the efficiency (rate coefficient) of the CO2-O vibrational energy transfer. For experimental ease the reverse reaction is used, i.e. collision of a vibrationally excited CO2 with atomic O, where we are able to convert to the atmospherically relevant reaction via a known equilibrium constant. The goal of this experiment was to measure the magnitudes of rate coefficients for vibrational energy states above the first excited state, a bending mode in CO2. An isotope of CO2, 13CO2, was used for experimental ease. The rate coefficients for given vibrational energy transfers in 13CO2 are not significantly different from 12CO2 at this level of precision. A slow-flowing gas mixture was flowed through a reaction cell: 13CO2 (vibrational specie of interest), O3(atomic O source), and Ar (bath gas). Transient diode laser absorption spectroscopy was used to monitor thechanging absorption of certain vibrational modes of 13CO2 after a UV pulse from a Nd:YAG laser was fired. Ozone absorbed the UV pulse in a process which vibrationally excited 13CO2 and liberated atomic O.Transient absorption signals were obtained by tuning the diode laser frequency to an appropriate ν3 transition and monitoring the population as a function of time following the Nd:YAG pulse. Transient absorption curves were obtained for various O atom concentrations to determine the rate coefficient of interest. Therotational states of the transitions used for detection were difficult to identify, though their short reequilibration timescale made the identification irrelevant for vibrational energy transfer measurements. The rate coefficient for quenching of the (1000) state was found to be (4 ± 8) x 10-12 cm3 s-1 which is the same order of magnitude as the lowest-energy bend-excited mode: (1.8 ± 0.3) x 10-12 cm3 s-1. More data is necessary before it can be certain that the numerical difference between the two is real.

Structure-Function Relations in the PI-PLC/GDPD Enzyme Superfamily

Phosphatidylinositol-specific phospholipases C (PI-PLC) are known to participate in many eukaryotic signal transduction pathways and act as virulence factors in lower organisms. Glycerophosphoryl diester phosphodiesterase (GDPD) enzymes are involved in phosphate homeostasis and phospholipid catabolism for energy production. Streptomyces antibioticus phosphatidylinositol-specific phospholipase C (SaPLC1) is a 38 kDa enzyme that displays characteristics of both enzyme superfamilies, representing an evolutionary link between these divergent enzyme classes. SaPLC1 also boasts a unique catalytic mechanism that involves a trans 1,6-cyclic inositol phosphate intermediate instead of the typical cis 1,2-cyclic inositol phosphate. The mechanism by which this occurs is still unclear. To attack this problem, we established a wide mutagenesis scan of the active site and measured activities of alanine mutants. A chemical rescue assay was developed to verify that the activity loss was due to the removal of the functional role of the mutated residue. 31P-NMR was employed in characterizing and quantifying intermediates in mutants that slowed the reaction sufficiently. We found that the H37A and H76A mutations support the hypothesis that these structurally conserved residues are also conserved in terms of their catalytic roles. H37 was found to be the general base (GB), while H76 plays the role of general acid (GA). K131 was identified as a semi-conserved key positive charge donor found at the entrance of the active site. By elucidating the SaPLC1 mechanism in relation to its active site architecture, we have increased our understanding of the structure-function relations that support catalysis in the PI-PLC/GDPD superfamily. These findings provide groundwork for in vivo studies of SaPLC1 function and its possible role in novel signaling or metabolism in Streptomyces.

Design Simulation for Solar Energy Research and Education

Solar research is primarily conducted in regions with consistent sunlight, severely limiting research opportunities in many areas. Unfortunately, the unreliable weather in Lewisburg, PA, can prove difficult for such testing to be conducted. As such, a solar simulator was developed for educational purposes for the Mechanical Engineering department at Bucknell University. The objective of this work was to first develop a geometric model to evaluate a one sun solar simulator. This was intended to provide a simplified model that could be used without the necessity of expensive software. This model was originally intended to be validated experimentally, but instead was done using a proven ray tracing program, TracePro. Analyses with the geometrical model and TracePro demonstrated the influence the geometrical properties had results, specifically the reflector (aperture) diameter and the rim angle. Subsequently, the two were approaches were consistent with one another for aperture diameters 0.5 m and larger, and for rim angles larger than 45°. The constructed prototype, that is currently untested, was designed from information provided by the geometric model, includes a metal halide lamp with a 9.5 mm arc diameter and parabolic reflector with an aperture diameter of 0.631 meters. The maximum angular divergence from the geometrical model was predicted to be 30 mRadians. The average angular divergence in TraceProof the system was 19.5 mRadians, compared to the sun’s divergence of 9.2 mRadians. Flux mapping in TracePro showed an intensity of 1000 W/m2 over the target plane located 40 meters from the lamp. The error between spectrum of the metal halide lamp and the solar spectrum was 10.9%, which was found by comparing their respective Plank radiation distributions. The project did not satisfy the original goal of matching the angular divergence of sunlight, although the system could still to be used for optical testing. The geometric model indicated performance in this area could be improved by increasing the diameter of the reflector, as well as decreasing the source diameter. Although ray tracing software provides more information to analyze the simulator system, the geometrical model is adequate to provide enough information to design a system.