Gradient estimates,Harnack inequalities and estimates for heat kernels of the sum of squares of vector fields

Research partially supported by NSF grant no. DMS-87-04209 and DMS-90-04062     

An efficient synthesis of an alphavbeta3 antagonist

A practical preparation of an alpha(v)beta(3) antagonist is reported. The antagonist consists of three key components, a tetrahydronaphthyridine moiety, a beta-alanine moiety, and a central imidazolidone moiety. The tetrahydronaphthyridine component was prepared using two different methods, both of which relied on variations of the Friedl?nder reaction to establish the desired regiochemistry. The beta-alanine component was prepared using Davies' asymmetric 1,4-addition methodology as the key stereo-defining step. The central imidazolidone portion was created from these two components using an effective three-step cyclization protocol. Thus, a highly convergent process for the drug candidate was defined.     

Depositing light in a photonic stop gap by use of Kerr nonlinear microresonators

We show theoretically that it is possible to trap light in a microresonator structure by use of four-wave mixing. The efficiency of the parametric process is substantially increased by the high group delay of light inside the structure. The energy that is trapped has a half-life of approximately 500 ps in the presence of both linear and nonlinear loss in the channel waveguides and resonators. We also demonstrate that the energy can be extracted from the cavity with a similar process.     

All-optical AND gate by use of a Kerr nonlinear microresonator structure

We numerically demonstrate the feasibility of constructing an all-optical AND gate by using a microresonator structure with Kerr nonlinearity. The gate is much smaller than similar AND gates based on Bragg gratings and has lower power requirements.     

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.