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.

Microscopic and Spectroscopic Methods for Probing the Clay Water Interface

Clay minerals have a fundamental importance in many processes in soils and sediments such as the bioavailability of nutrients, water retention, the adsorption of common pollutants, and the formation of an impermeable barrier upon swelling. Many of the properties of clay minerals are due to the unique environment present at the clay mineral/water interface. Traditional techniques such as X-ray diffraction (XRD) and absorption isotherms have provided a wealth of information about this interface but have suffered from limitations. The methods and results presented herein are designed to yield new experimental information about the clay mineral/water interface.A new method of studying the swelling dynamics of clay minerals was developed using in situ atomic force microscopy (AFM). The preliminary results presented here demonstrate that this technique allows one to study individual clay mineral unit layers, explore the natural heterogeneities of samples, and monitor swelling dynamics of clay minerals in real time. Cation exchange experiments were conducted monitoring the swelling change of individual nontronite quasi-crystals as the chemical composition of the surrounding environment was manipulated several times. A proof of concept study has shown that the changes in swelling are from the exchange of interlayer cations and not from the mechanical force of replacing the solution in the fluid cell. A series of attenuated total internal reflection Fourier transform infrared spectroscopy (ATR-FTIR) experiments were performed to gain a better understanding of the organization of water within the interlayer region of two Fe-bearing clay minerals. These experiments made use of the Subtractive Kramers-Kronig (SKK) Transform and the calculation of difference spectra to obtain information about interfacial water hidden within the absorption bands of bulk water. The results indicate that the reduction of structural iron disrupts the organization of water around a strongly hydrated cation such as sodium as the cation transitions from an outer-sphere complex with the mineral surface to an inner-sphere complex. In the case of a less strongly hydrated cation such as potassium, reduction of structural iron actually increases the ordering of water molecules at the mineral surface. These effects were only noticed with the reduction of iron in the tetrahedral sheet close to the basal surface where the increased charge density is localized closer to the cations in the interlayer.

Enzymatic Activity of Soybean Lipoxygenase-1 on Linoleoyl-Derivatized Agarose

Soybean lipoxygenase-1 (SBLO-1) catalyzes the oxygenation of linoleic acid to form 13(S) and 9(R) hydroperoxides. The manner in which substrates bind to the lipoxygenase family of enzymes is not known. It is believed fatty acid substrates may bind either with the aliphatic end first or with the carboxylate group facing the interior of the protein. This thesis tested a potential methyl-end first substrate binding mechanism by studying the activity of SBLO-1 to oxygenate immobilized linoleoyl residues attached to an insoluble polymer. Linoleic acid was attached to aminohexyl agarose in the presence of N-(3- dimethylaminopropyl)-N’-ethylcarbodiimide hydrochloride (EDC) and Nhydroxysuccinimide (NHS). The concentration of the covalently attached residues was facilitated by enriching linoleic acid with a small amount of the radioactive 14C-isotope. Functionalization yields of 3% available primary amines on the resin were obtained. Enzymatic oxygenation of the linoleoyl-residues was verified using the ferrous oxidation in xylenol orange (FOX) assay. Approximately 30% of the attached linoleoyl moieties were converted to hydroperoxides in the presence of SBLO-1. A disulfide-containing cleavable linker, cystamine, was used as part of an improved method to isolate the product in a facile manner. Cystamine was attached to NHS-activated agarose with approximately 5% overall functionalization yield of available functional groups. 14C-linoleic acid was successfully covalently linked to the cystamine moieties in the presence of EDC and NHS. The FOX assay verified the enzymatic oxygenation of the linoleoyl residues attached to cystamine-derivatized agarose. The isolation of the peroxide product was attempted in a series of extractions in organic solvents. The product was analyzed using GC/MS which did not show a new peak indicative of product. Further work is needed to successfully analyze the stereoand regiochemistry of the oxygenated product. The presence of the peroxides in this study indicated the linoleoyl residues behave as substrates of SBLO-1. It is unknown how bulky substrates bind to the active site; however, it is difficult to rationalize a carboxylate group-first binding mode. Discovery of the 13(S)-hydroperoxide product on the linoleoyl-agarose would support the claim of a potential methyl-end first binding mechanism.

The Modified Direct Analysis Method: an Extension of the Direct Analysis Method

The purpose of this research project is to study an innovative method for the stability assessment of structural steel systems, namely the Modified Direct Analysis Method (MDM). This method is intended to simplify an existing design method, the Direct Analysis Method (DM), by assuming a sophisticated second-order elastic structural analysis will be employed that can account for member and system instability, and thereby allow the design process to be reduced to confirming the capacity of member cross-sections. This last check can be easily completed by substituting an effective length of KL = 0 into existing member design equations. This simplification will be particularly useful for structural systems in which it is not clear how to define the member slenderness L/r when the laterally unbraced length L is not apparent, such as arches and the compression chord of an unbraced truss. To study the feasibility and accuracy of this new method, a set of 12 benchmark steel structural systems previously designed and analyzed by former Bucknell graduate student Jose Martinez-Garcia and a single column were modeled and analyzed using the nonlinear structural analysis software MASTAN2. A series of Matlab-based programs were prepared by the author to provide the code checking requirements for investigating the MDM. By comparing MDM and DM results against the more advanced distributed plasticity analysis results, it is concluded that the stability of structural systems can be adequately assessed in most cases using MDM, and that MDM often appears to be a more accurate but less conservative method in assessing stability.

Application of Discrete Fourier Inter-Coefficient Difference for Assessing Genetic Sequence Similarity

Digital signal processing (DSP) techniques for biological sequence analysis continue to grow in popularity due to the inherent digital nature of these sequences. DSP methods have demonstrated early success for detection of coding regions in a gene. Recently, these methods are being used to establish DNA gene similarity. We present the inter-coefficient difference (ICD) transformation, a novel extension of the discrete Fourier transformation, which can be applied to any DNA sequence. The ICD method is a mathematical, alignment-free DNA comparison method that generates a genetic signature for any DNA sequence that is used to generate relative measures of similarity among DNA sequences. We demonstrate our method on a set of insulin genes obtained from an evolutionarily wide range of species, and on a set of avian influenza viral sequences, which represents a set of highly similar sequences. We compare phylogenetic trees generated using our technique against trees generated using traditional alignment techniques for similarity and demonstrate that the ICD method produces a highly accurate tree without requiring an alignment prior to establishing sequence similarity.