A Domain Embedding Method Using the Optimal Distributed Control and a Fast Algorithm

We propose a domain embedding method to solve second order elliptic problems in arbitrary two-dimensional domains. The method is based on formulating the problem as an optimal distributed control problem inside a disc in which the arbitrary domain is embedded. The optimal distributed control problem inside the disc is solved rapidly using a fast algorithm developed by Daripa et al. [3,7,10–12]. The arbitrary domains can be simply or multiply connected and the proposed method can be applied, in principle, to a large number of elliptic problems. Numerical results obtained for Dirichlet problems associated with the Poisson equation in simply and multiply connected domains are presented. The computed solutions are found to be in good agreement with the exact solutions with moderate number of grid points in the domain.     

Lewis Acid-Promoted Mukaiyama Aldol-Prins (MAP) Cyclizations of Acetals, Ketals, α-Acetoxy Ethers, and Orthoformates

The Mukaiyama aldol-Prins (MAP) cyclization of acetals stereoselectively provided substituted tetrahydropyrans. The scope of the reaction has been expanded to include other electrophiles, including ketals and α-acetoxy ethers. Finally, a double MAP cyclization with orthoformates is described.     

Further Development and Validation of the Teaching Science as Inquiry (TSI) Instrument

The purpose of this study was to further develop and validate the Teaching Science as Inquiry (TSI) Instrument, an instrument designed to measure the self‐efficacy beliefs of preservice teachers in regards to the teaching of science as inquiry. Based on the validation processes and the associated data analysis, the TSI demonstrates continued content and construct validity with high internal reliability when used with prospective elementary science teachers.     

Industrial applications of supercritical fluid chromatography: polymer analysis

Summary Polymers can be difficult to fully characterize by conventional chromatographic methods [i.e., gas chromatography (GC), high performance liquid chromatography (HPLC) and size exclusion chromatography (SEC)] due to temperature instability, detector incompatibility, nonvolatility, molecular weight considerations or insufficient chromatographic efficiency. Capillary supercritical fluid chromatography (SFC) offers several advantages for polymer analysis. Complex distributions can be resolved, low temperatures can be used and individual oligomers can be detected, allowing differences in molecular weight distributions to be quantitatively and qualitatively measured. In this paper, results will be shown for the analysis of various types of polymers demonstrating how changes in chromatographic parameters affect the analysis

---

Industrielle Anwendungen der Chromatographie mit überkritischen fluiden Phasen: Polymeranalyse

     

Effect of masker-frequency variability on the detection performance of infants and adults

The effect of masker-frequency variability on the detection performance of 7-9 month-old infants and adults was examined. Listeners detected a 300-ms 1000-Hz pure tone masked by: (1) A random-frequency two-tone complex; (2) a fixed-frequency two-tone complex; or (3) a broadband noise. Maskers repeated at 300-ms intervals throughout testing at 60 dB SPL. The signal was presented simultaneously with one presentation of the masker. Thresholds were determined adaptively using an observer-based method. Infants' thresholds were higher than adults' in all conditions, but infants' and adults' thresholds changed with masker condition in qualitatively similar ways. The fixed two-tone complex produced masking for both age groups, but more masking for infants than for adults. For infants and adults, the random two-tone complex produced more masking than broadband noise, but the difference was greater for infants than for adults. For infants and adults, the random two-tone complex produced more masking than the fixed two-tone complex, and the difference between these conditions was similar for both age groups. These results suggest that infants are more susceptible to informational masking than adults in the absence of spectral variability. Whether infants are more susceptible to the effects of masker-frequency variability than adults remains to be clarified.     

Non-aqueous solvation of n-octanol and ethanol: spectroscopic and computational studies

Raman spectroscopy was used to examine the interactions of the free O-H bonds in n-octanol and ethanol with the organic solvents carbon tetrachloride (CCl(4)), cyclohexane, and benzene. These spectra reveal that the solvents CCl(4) and cyclohexane have a small effect on the free O-H peak of alcohols, whereas benzene as a solvent significantly red-shifts the free O-H band. Calculated spectra were generated via MP2/6-31G* calculations and the B3LYP/6-31+G**//MP2/6-31G*-derived Boltzmann populations of each ethanol complex and are consistent with the experimental results. Additional spectra were calculated using Boltzmann populations derived from single-point energies at the polarizable continuum model (PCM) level with the B3LYP/6-31+G** level of theory to take overall solvent effects into account, and these simulated spectra are also largely consistent with the experimental results. Analysis of the computational results reveals a lengthening of the O-H bond from the O-H interaction with the delocalized electronic structure of benzene as well as a bimodal distribution of the free O-H peak of the alcohol/benzene mixtures due to two distinctly different types of alcohol/benzene complexes.     

Single DNA molecule stretching in sudden mixed shear and elongational microflows

High-throughput stretching and monitoring of single DNA molecules in continuous elongational flow offers compelling advantages for biotechnology applications such as DNA mapping. However, the polymer dynamics in common microfluidic implementations are typically complicated by shear interactions. These effects were investigated by observation of fluorescently labeled 185 kb bacterial artificial chromosomes in sudden mixed shear and elongational microflows generated in funneled microfluidic channels. The extension of individual free DNA molecules was studied as a function of accumulated fluid strain and strain rate. Under constant or gradually changing strain rate conditions, stretching by the sudden elongational component proceeded as previously described for an ideal elongational flow (T. T. Perkins, D. E. Smith and S. Chu, Science, 1997, 276, 2016): first, increased accumulated fluid strain and increased strain rate produced higher stretching efficiencies, despite the complications of shear interactions; and second, the results were consistent with unstretched molecules predominantly in hairpin conformations. More abrupt strain rate profiles did not deliver a uniform population of highly extended molecules, highlighting the importance of balance between shear and elongational components in the microfluidic environment for DNA stretching applications. DNA sizing with up to 10% resolution was demonstrated. Overall, the device delivered 1000 stretched DNA molecules per minute in a method compatible with diffraction-limited optical sequence motif mapping and without requiring laborious chemical modifications of the DNA or the chip surface. Thus, the method is especially well suited for genetic characterization of DNA mixtures such as in pathogen fingerprinting amidst high levels of background DNA.     

ABC and the Hasse principle for quadratic twists of hyperelliptic curves

Conditionally on the ABC conjecture, we apply work of Granville to show that a hyperelliptic curve $C_{/\mathbb{Q}}$ of genus at least three has infinitely many quadratic twists that violate the Hasse Principle iff it has no $\mathbb{Q}$-rational hyperelliptic branch points.