Density computations for real quadratic units

In order to study the density of the set of positive integers for which the negative Pell equation is solvable in integers, we compute the norm of the fundamental unit in certain well-chosen families of real quadratic orders. A fast algorithm that computes 2-class groups rather than units is used. It is random polynomial-time in as the factorization of is a natural part of the input for the values of we encounter. The data obtained provide convincing numerical evidence for the density heuristics for the negative Pell equation proposed by the second author. In particular, an irrational proportion of the real quadratic fields without discriminantal prime divisors congruent to 3 mod 4 should have a fundamental unit of norm .

     

A velocity program using the Kanade–Lucas–Tomasi feature-tracking algorithm with demonstration for pressure and electroosmosis conditions

Investigating microfluidic flow profiles is of interest in the microfluidics field for the determination of various characteristics of a lab-on-a-chip system. Microparticle tracking velocimetry uses computational methods upon recording video footage of microfluidic flow to ultimately visualize motion within a microfluidic system across all frames of a video. Current methods are computationally expensive or require extensive instrumentation. A computational method suited to microparticle tracking applications is the robust Kanade–Lucas–Tomasi (KLT) feature-tracking algorithm. This work explores a microparticle tracking velocimetry program using the KLT feature-tracking algorithm. The developed program is demonstrated using pressure-driven and EOF and compared with the respective mathematical fluid flow models. An electrostatics analysis of EOF conditions is performed in the development of the mathematical using a Poisson's Equation solver. This analysis is used to quantify the zeta potential of the electroosmotic system. Overall, the KLT feature-tracking algorithm presented in this work proved to be highly reliable and computationally efficient for investigations of pressure-driven and EOF in a microfluidic system.     

Spectroscopic and time-dependent density functional investigation of the role of structure on the acid-base effects of citrinin detection

A time-dependent density functional theory (TD-DFT) study was carried out on tautomers of the mycotoxin citrinin in the neutral, anionic, and cationic forms to gain insight into the role of chemical structure on detection. Steady-state fluorescence studies of citrinin in micellar aqueous solutions produced unusual results for ionic surfactants and the neutral Triton X-100 enhanced fluorescence emission. Ground-state and time-dependent density functional studies were carried out on five tautomers of citrinin using the B3LYP density functional and the 6-311+G(2df,2p) basis set. The investigation revealed that deprotonation is a major factor governing the shifts in fluorescence excitation and emission maxima. Moreover, the position of the lowest unoccupied molecular orbitals is removed from the fluorophore moiety of citrinin in the dianionic state which is consistent with the diminished fluorescence of the toxin in basic solutions. The ionic characteristics of certain chemosensors can influence the structure and intrinsic spectroscopic properties of citrinin.     

Deoxygenation of Aromatic Ketones Using Transfer Hydrogenolysis with Raney Nickel in 2-Propanol

Aryl ketones are readily deoxygenated to their corresponding aryl alkanes upon treatment with Raney nickel catalyst in boiling 2-propanol.

Two capacitive windows in a rectangular wave guide

Summary The behaviour of two capacitive windows in a rectangular wave guide, located at small distances apart in comparison with the wave length, is investigated. The three-dimensional problem is reduced to a two-dimensional one. Two simultaneous integral equations for the electric field intensities in the apertures are derived. A solution for these unknown quantities can be obtained, representing them by a Fourier series and approximating the kernel functions. Expressions for the reflection and transmission coefficients are given. Absolute values of the transmission coefficient are obtained, both theoretically and experimentally.     

Loop grafting of Bacillus subtilis lipase A: inversion of enantioselectivity

Lipases are successfully applied in enantioselective biocatalysis. Most lipases contain a lid domain controlling access to the active site, but Bacillus subtilis Lipase A (LipA) is a notable exception: its active site is solvent exposed. To improve the enantioselectivity of LipA in the kinetic resolution of 1,2-O-isopropylidene-sn-glycerol (IPG) esters, we replaced a loop near the active-site entrance by longer loops originating from Fusarium solani cutinase and Penicillium purpurogenum acetylxylan esterase, thereby aiming to increase the interaction surface for the substrate. The resulting loop hybrids showed enantioselectivities inverted toward the desired enantiomer of IPG. The acetylxylan esterase-derived variant showed an inversion in enantiomeric excess (ee) from -12.9% to +6.0%, whereas the cutinase-derived variant was improved to an ee of +26.5%. The enantioselectivity of the cutinase-derived variant was further improved by directed evolution to an ee of +57.4%.     

Determination of the preferred conformation of the bicyclic Galerucella pheromone using density functional theory optimization and calculations of chemical shifts

A pheromone from the beetle, Galerucella calmariensis, was recently isolated and identified (Bartelt, R. J. et al. J. Chem. Ecol. 2006, 32, 693-712) as a 14-carbon, bicyclic dimethylfuran lactone, with the systematic name 12,13-dimethyl-5,14-dioxabicyclo[9.2.1]tetradeca-1(13),11-dien-4-one. The main 12-membered lactone ring is very flexible; as a result, there exist multiple possible conformations. The preferred conformation cannot be deduced solely from room-temperature NMR measurements. Using density functional (DFT) studies, 26 unique conformers with energies within 10.0 kcal/mol of the global minimum-energy structure were found. A mirror-image plane exists so that each conformer has an "inverse" structure with the same energy, for which the dihedral angles around the flexible ring have opposite sign. The isotropic 1H and 13C NMR chemical shifts of the DFT-optimized structures were calculated using the gauge-including atomic orbital (GIAO) method. By considering the relative energies of the conformers and the calculated and observed NMR spectra, we concluded that the molecule exists primarily as a mixture of two distinct conformers at room temperature, each being present with its mirror-image inverse. Structural interconversions among these likely occur on a time scale that is fast compared to the NMR experiments. Using mode-following and dihedral-driving techniques, several potential pathways were found for the conversion of the lowest-energy conformer to its mirror-image structure. Ab initio molecular dynamics (AIMD) using the 4-31G basis set was carried out for 50 ps to test the availability of various low-energy minima and the transition states found from the searches noted above.     

Preparation of monodisperse, fluorescent PMMA-latex colloids by dispersion polymerization

We report a single step procedure to prepare monodisperse colloidal poly(methyl)methacrylate (PMMA) particles where fluorescent dyes are incorporated into the polymer network. The particles are sterically stabilized against flocculation by poly(12-hydroxystearic acid). The fluorescent dyes are RITC (rhodamine isothiocyanate)-aminostyrene (RAS) and 4-methylaminoethylmethacrylate-7-nitrobenzo-2-oxa-1,3-diazol (NBD-MAEM), which are prepared from (commercially available) RITC and 4-chloro-7-nitrobenzo-2-oxa-1,3-diazol (NBD-Cl), respectively, as starting materials. The particles can be grown larger with nonfluorescent PMMA. Examples of the usefulness of these model particles in colloid science are given.