Equivalences between isolated hypersurface singularities

Research by this author supported in part by N.S.F. Grant No. DMS-84114477     

Energy extraction of Porro resonator in Pockels cell Q-switch operation

Deviation of a practical Pockels cell Q-switch bias voltage from the ideal bias value significantly affects the extraction of useful output energy. The losses of two practical bias voltages are calculated and the properly rotated angle towards the right-hand side prism of the Porro resonator is determined to simulate the different losses. The losses are due to deviation of the Q-switch bias voltage from the ideal value. It not only degrades the useful output energy, but introduces a useless energy loss in the reverse output direction. For the different losses of these two practical Pockels cell bias voltages, the useful output energy difference is about 30%. The useful output energy and lost energy ratios of the two equivalent loss configurations are 0.54 and 0.89, respectively. These ratios agreed quite well with the theoretical results.     

On the construction of a nonlinear recursive predictor

In this paper, we present a novel approach for constructing a nonlinear recursive predictor. Given a limited time series data set, our goal is to develop a predictor that is capable of providing reliable long-term forecasting. The approach is based on the use of an artificial neural network and we propose a combination of network architecture, training algorithm, and special procedures for scaling and initializing the weight coefficients. For time series arising from nonlinear dynamical systems, the power of the proposed predictor has been successfully demonstrated by testing on data sets obtained from numerical simulations and actual experiments.     

Phase Conjugation with Picosecond Pulses in BaTi03

The self-pumped phase conjugate signal of picosecond laser pulses is observed. The width of the incident laser pulses is about 1.5 ps and their repetition rate is 82 MHz. The wavelength of the pulses can be tuned in the range from 710 nm to 850 nm. The pulse character of the conjugate signal is determined by an autocorrelator. The quality of the conjugate pulses is found to be good by the well-known phase distorter method.     

Rota–Baxter Hom-Lie–Admissible Algebras

We study Hom-type analogs of Rota–Baxter and dendriform algebras, called Rota–Baxter G-Hom–associative algebras and Hom-dendriform algebras. Several construction results are proved. Free algebras for these objects are explicitly constructed. Various functors between these categories, as well as an adjunction between the categories of Rota–Baxter Hom-associative algebras and of Hom-(tri)dendriform algebras, are constructed.     

Large-volume sample stacking with polarity switching for the analysis of bacteria by capillary electrophoresis with laser-induced fluorescence detection

Capillary electrophoresis has been utilized for the rapid analysis of bacteria under specific experimental conditions. In this work, a method of large-volume sample stacking with polarity switching was evaluated for the analysis of bacteria by capillary electrophoresis with laser-induced fluorescence detection in order to enhance the detection sensitivity. The results indicated that the proposed method is not only effective for the focusing of bacterial cells, but also for the separation of mixtures of bacteria. With the optimized conditions, an enhancement factor of around 60-fold was obtained when long sample plug (up to 39.6% of capillary volume) was injected. Moreover, with the help of such stacking method, single, sharp, intense peak with high efficiency was observed without multiple peaks attributable to irregular clusters and aggregates of bacterial cells. This simple stacking approach appears to be promising as a rapid sterility test in various fields of applications.     

Direct alpha-oxytosylation of carbonyl compounds: one-pot synthesis of heterocycles

N-Methyl-O-tosylhydroxylamine is an effective reagent for the direct alpha-oxytosylation of carbonyl compounds. The reactions proceed smoothly at room temperature in the presence of both moisture and air and functional group tolerance in the substrate is good. With nonsymmetrical substrates regioselectivity for primary over secondary centers is observed and complete regiospecificity for primary over tertiary centers is obtained. Addition of a bis-heteronucleophile directly to the crude reaction mixture in a one-pot process leads to the corresponding heterocyclic product.