Second order differential inequalities in the complex plane

Let w(z) be regular in the unit disk U and let h(r, s, t) be a complex function defined in a domain of C³. The authors determine conditions on h such that $\text{¦ h(w(z), zw′(z), z}{}^2\text{w″(z))¦ < 1}$ implies $\text{¦ w(z)¦ < 1}$ and such that Re h(w(z), zw′(z), z²w″(z)) > 0 implies Re w(z) > 0. Applications of these results to univalent function theory, differential equations and harmonic functions are given.     

The influence of grating characteristics on moiré fringe multiplication

Coherent optical techniques of fringe multiplication can be used to enhance the sensitivity of moiré measurements. However, for some coherent optical-processing systems, the significance of the resulting interference pattern is influenced by the characteristics of the gratings being processed. Analysis of one commonly used system for fringe multiplication involving two bar and space amplitude gratings reveals that accuracy of displacements and strains calculated from a fringe pattern is very sensitive to the transmission ratios of the gratings being processed. For variations of the transmission ratio of only 10 percent from the ideal case of 50 percent, the interference patterns produced by optical processing no longer correspond to multiplied moiré-fringe patterns.     

Environmental bioremediation for organometallic compounds: Microbial growth and arsenic volatillization from soil and retorted shale

Nutrient effects on microbial growth and arsenic volatilization from retorted oil shale and soil were evaluated in a laboratory study. Dimethylarsinic acid (DMAA), methanearsonic acid (MAA) and sodium arsenate amendments were used with added nutrients, or with retort process water added to simulate possible co-disposal conditions. In experiments with soil and retorted shale, dimethylarsinic acid showing the highest cumulative arsenic releases, in comparison with added inorganic sodium arsenate (SA). Low but detectable amounts of innate arsenic present in retorted shale could be volatilized with added organic matter. In soil, arsenic volatilization showed a direct relationship to nutrient levels and microbial growth. With shale, in comparison, a threshold response to available nutrients was evident. Distinct increases in fungal community development occurred with nutrients available at a level of 2.5% w/v, which also allowed incresed arsenic volatization. Codisposal of retort process waters with shale allowed arsenic volatilization without the addition of other nutrients. The presence of retort process water limited arsenic volatilization from the added organometallic compounds DMAA and MAA, but not from SA or innate arsenic. These differences should be useful in the definition of permissive and non-permissive environmental conditions for arsenic volatilization in bioremediation programs.     

Incremented alkyl derivatives enhance collision induced glycosidic bond cleavage in mass spectrometry of disaccharides

Electrospray ionization and collision induced dissociation on a triple quadrupole mass spectrometer were used to determine the effect of spatial crowding of incremented alkyl groups of two anomeric pairs of peralkylated (methyl to pentyl) disaccharides (maltose/cellobiose and isomaltose/gentiobiose). Protonated molecules were generated which underwent extensive fragmentation under low energy conditions. For both the 1 --> 4 and 1 --> 6 alpha and beta isomers, at comparable collision energies the methyl derivative exhibited the least fragmentation followed by ethyl, propyl, butyl, and pentyl. Collision energy is converted to rotational-vibrational modes in competition with bond cleavage, as represented by the slope of product/parent ion (D/P) ratio versus offset energy. Variable rotational freedom at the glycosidic linkage with incremented alkyl groups is hypothesized to be responsible for this effect. Discrimination of anomeric configuration was also assessed for these stereoiosmeric disaccharides. A systematic study showed that an increasing discrimination was attained for the 1 --> 4 isomeric pair as the size of the derivative increased from methyl to pentyl. No anomeric discrimination was attained for the 1 --> 6 isomeric pair. Parent and product ion scans confirmed the consistency of fragmentation pathways among derivatives. Chem-X and MM3 molecular modeling programs were used to obtain minimum energy structures and freedom of motion volumes for the permethylated disaccharides. The modeling results correlated with the fragmentation ratios obtained in the mass spectrometer giving strong indication that the collision induced spectra are dependent on the freedom of rotational motion around the glycosidic bond.     

UV Raman demonstrates that alpha-helical polyalanine peptides melt to polyproline II conformations

We examined the 204-nm UV Raman spectra of the peptide XAO, which was previously found by Shi et al.'s NMR study to occur in aqueous solution in a polyproline II (PPII) conformation. The UV Raman spectra of XAO are essentially identical to the spectra of small peptides such as ala(5) and to the large 21-residue predominantly Ala peptide, AP. We conclude that the non-alpha-helical conformations of these peptides are dominantly PPII. Thus, AP, which is highly alpha-helical at room temperature, melts to a PPII conformation. There is no indication of any population of intermediate disordered conformations. We continued our development of methods to relate the Ramachandran Psi-angle to the amide III band frequency. We describe a new method to estimate the Ramachandran Psi-angular distributions from amide III band line shapes measured in 204-nm UV Raman spectra. We used this method to compare the Psi-distributions in XAO, ala(5), the non-alpha-helical state of AP, and acid-denatured apomyoglobin. In addition, we estimated the Psi-angle distributions of peptide bonds which occur in non-alpha-helix and non-beta-sheet conformations in a small library of proteins.     

Nano- sensing and catalysis technologies for managing food-water-energy (FEW) resources in farming

As the world population grows and new environmental, sustainability, and security challenges emerge, it becomes critical to consider and propose solutions for problems at the nexus of Food, Water, and Energy (FEW). These three are key resources critical for the human health and welfare. Managing effectively the FEW resources in the context of farming, while focusing on lactation cattle, is the theme of this work. The solutions presented here are based on nano-sensing and catalysis. Novel gas sensing technologies are described that can monitor the health of the livestock, monitor the feed conversion efficiency in their feed, and help reduce the water footprint related to the production of animal products (such as milk). Water quality control and water clean-up technologies along with energy harvesting tools based on nanofibrous mats are also presented; these help reduce the carbon footprint of the farming processes. Implementing these integrated systems in any agricultural facility will promote the sustainable production of meat and meat products.     

Dependence of glycine CH2 stretching frequencies on conformation, ionization state, and hydrogen bonding

We experimentally and theoretically examined the conformation, pH, and temperature dependence of the CH2 stretching frequencies of glycine (gly) in solution and in the crystalline state. To separate the effects of the amine and carboxyl groups on the CH2 stretching frequencies we examined the Raman spectra of 2,2,2-d3-ethylamine (CD3-CH2-NH2) and 3,3,3-d3-propionic acid (CD3-CH2-COOH) in D2O. The symmetric (nusCH2) and asymmetric (nuasCH2) stretching frequencies show a significant dependence on gly conformation. We quantified the relation between the frequency splitting (Delta = nuasCH2-nusCH2) and the xi angle which determines the gly conformational geometry. This relation allows us to determine the conformation of gly directly from the Raman spectral frequencies. We observe a large dependence of the nusCH2 and nuasCH2 frequencies on the ionization state of the amine group, which we demonstrate theoretically results from a negative hyperconjugation between the nitrogen lone pair and the C-H antibonding orbitals. The magnitude of this effect is maximized for C-H bonds trans to the nitrogen lone pair. In contrast, a small dependence of the CH2 stretching frequencies on the carboxyl group ionization state arises from delocalization of electron density from carboxyl oxygen to C-H bonding orbitals. According to our experimental observations and theoretical calculations the temperature dependence of the nusCH2 and nuasCH2 of gly is due to the change in the hydrogen-bonding strength of the amine/carboxyl groups to water.     

Role of the geometry, restricted rotations and solvents on the computed 2,2'-diphenyl-1-picrylhydrazyl hyperfine tensors

The nuclear hyperfine tensor (A) components of the 2,2'-diphenyl-1-picrylhydrazyl neutral radical are computed using the UB1LYP hybrid density functional method. Solvent interactions via hydrogen bonding are found to play a crucial role in the position of the two phenyl rings relative to the picryl moiety. Under these conditions, the calculated isotropic hyperfine tensor components of the N 1 and N 2 hydrazyl backbone are within approximately 1.3 Gauss (G) of the experimental values determined by EPR and ENDOR spectroscopy. Just as important are the effects of restricted rotations of the phenyl rings on these tensors. Rotational averaging using a Maxwell-Boltzmann type distribution improves the agreement between theory and experiment to less than 1.0 G. In addition, rotational averaging of the twelve isotropic proton coupling constants has also been performed. They come within 0.3 G of the experimental values. Thus, for the first time, all the nuclear hyperfine tensor components of this large class of molecules are accurately calculated without resorting to post Hartree-Fock techniques.     

Unusually stable palladium(IV) complexes: detailed mechanistic investigation of C-O bond-forming reductive elimination

This communication describes the synthesis of a family of unusually stable palladium(IV) complexes containing two chelating 2-phenylpyridine ligands and two benzoates. These complexes undergo clean C-O bond-forming reductive elimination upon heating, and the mechanism of this catalytically relevant process has been studied in detail. Solvent effects, crossover experiments, Eyring plots (which show DeltaS of -1.4 +/- 1.9 and 4.2 +/- 1.4 in CDCl3 and DMSO, respectively), and Hammett analysis (which shows rho = -1.36 +/- 0.04 upon substitution of the para-benzoate substituent) all suggest that reductive elimination does not proceed via initial dissociation of a benzoate ligand. Instead, an unusual mechanism involving pre-equilibrium dissociation of the N-arm of the phenylpyridine ligand is proposed.     

Tracking excited state dynamics with coherent control: automated limiting of population transfer in LDS750

Closed loop automated pulse shaping experiments are conducted to investigate population transfer in solutions of the laser dye LDS750 in acetonitrile and ethanol. Guided by a genetic algorithm, the optical phases of broadband noncollinear parametric amplifier pulses are modulated by a micromachined deformable mirror to minimize sample fluorescence. The objectives were to test if nonlinearly chirped pulses could reduce population transfer below levels attained by their linearly chirped analogues, and if so, whether the resulting pulse shapes could be rationalized in terms of the photoinduced molecular dynamics. We further aimed to discover how the optimal solutions depend on the pulse fluence, and on the nature of the solvent. Using frequency resolved optical gating, the optimal field is shown to consist of a transform limited blue portion, which promotes population to the excited state, and a negatively chirped red tail, which follows the Stokes shifting of the excited density and dumps it back down to the ground state through stimulated emission. This is verified by comparing the optimal group delay dispersion with multichannel transient absorption data collected in acetonitrile. The optimal pulse shape was not significantly affected by variation of pulse fluence or by the change of solvent for the two polar liquids investigated. These results are discussed in terms of accumulated insights concerning the photophysics of LDS750 and the capabilities of our learning feedback scheme for quantum control.