Application of mid-infrared cavity-ringdown spectroscopy to trace explosives vapor detection using a broadly tunable (6–8 μm) optical parametric oscillator

A novel instrument, based on cavity-ringdown spectroscopy (CRDS), has been developed for trace gas detection. The new instrument utilizes a widely tunable optical parametric oscillator (OPO), which incorporates a zinc–germanium–phosphide (ZGP) crystal that is pumped at 2.8 μm by a 25-Hz Er,Cr:YSGG laser. The resultant mid-IR beam profile is nearly Gaussian, with energies exceeding 200 μJ/pulse between 6 and 8 μm, corresponding to a quantum conversion efficiency of approximately 35%. Vapor-phase mid-infrared spectra of common explosives (TNT, TATP, RDX, PETN and Tetryl) were acquired using the CRDS technique. Parts-per-billion concentration levels were readily detected with no sample preconcentration. A collection/flash-heating sequence was implemented in order to enhance detection limits for ambient air sampling. Detection limits as low as 75 ppt for TNT are expected, with similar concentration levels for the other explosives. Received: 1 April 2002 / Revised version: 13 June 2002 / Published online: 12 September 2002 RID="*" ID="*"Corresponding author. Fax: +1-408/524-0551, E-mail: mtodd@picarro.com     

Gaps between integers with the same prime factors

We give numerical and theoretical evidence in support of the conjecture of Dressler that between any two positive integers having the same prime factors there is a prime. In particular, it is shown that the abc conjecture implies that the gap between two consecutive such numbers is , and it is shown that this lower bound is best possible. Dressler's conjecture is verified for values of and up to .

     

Selective ultrafilters and

Mathias (Happy families, Ann. Math. Logic. 12 (1977), 59-111) proved that, assuming the existence of a Mahlo cardinal, it is consistent that CH holds and every set of reals in is -Ramsey with respect to every selective ultrafilter . In this paper, we show that the large cardinal assumption cannot be weakened.

     

Engineering quadrupole magnetic flow sorting for the isolation of pancreatic islets

Quadrupole magnetic flow sorting (QMS) is being adapted from the separation of suspensions of single cells (<15 μm) to the isolation of pancreatic islets (150–350 μm) for transplant. To achieve this goal, the critical QMS components have been modeled and engineered to optimize the separation process. A flow channel has been designed, manufactured, and tested. The quadrupole magnet assembly has been designed and verified by finite element analysis. Pumps have been selected and verified by test. Test data generated from the pumps and flow channel demonstrate that the fabricated channel and peristaltic pumps fulfill the requirements of successful QMS separation.     

The hierarchical basis multigrid method

Summary We derive and analyze the hierarchical basis-multigrid method for solving discretizations of self-adjoint, elliptic boundary value problems using piecewise linear triangular finite elements. The method is analyzed as a block symmetric Gauß-Seidel iteration with inner iterations, but it is strongly related to 2-level methods, to the standard multigridV-cycle, and to earlier Jacobi-like hierarchical basis methods. The method is very robust, and has a nearly optimal convergence rate and work estimate. It is especially well suited to difficult problems with rough solutions, discretized using highly nonuniform, adaptively refined meshes.     

Extensions of Lemke's algorithm for the linear complementarity problem

Lemke's algorithm for the linear complementarity problem fails when a desired pivot is not blocked. A projective transformation overcomes this difficulty. The transformation is performed computationally by adjoining a new row to a schema of the problem and pivoting on the element in this row and the unit constant column. Two new algorithms result; some conditions for their success are discussed.This research was partially supported by National Science Foundation, Grant GK-42092.     

Coulomb-nuclear interference for inelastic deuteron scattering

The interference between Coulomb excitation and nuclear excitation has been observed for ^{54, 56}Fe, ⁶⁰Ni, ¹¹⁴Cd, ¹⁵²Sm, and ¹⁹²Os by measuring excitation functions of elastic and inelastic deuteron scattering at back angles. The interference is strongly constructive, indicating a predominantly imaginary nuclear form factor. DWBA calculations using the collective model, although predicting constructive interference, are unable to predict the magnitude of the observed effect.