Ortho-Babinet polarization-interrogating filter: an interferometric approach to polarization measurement

A novel, interferometric, polarization-interrogating filter assembly and method for the simultaneous measurement of all four Stokes parameters across a partially polarized irradiance image in a no-moving-parts, instantaneous, highly sensitive manner is described. In the reported embodiment of the filter, two spatially varying linear retarders and a linear polarizer comprise an ortho-Babinet, polarization-interrogating (OBPI) filter. The OBPI filter uniquely encodes the incident ensemble of electromagnetic wave fronts comprising a partially polarized irradiance image in a controlled, deterministic, spatially varying manner to map the complete state of polarization across the image to local variations in a superposed interference pattern. Experimental interferograms are reported along with a numerical simulation of the method.     

Characterizing and monitoring respiratory aerosols by light scattering

The elastic-scattering intensity pattern from a single particle as a function of spherical coordinate angles theta and phi provides detailed information on the pattern's morphology. By use of an ellipsoidal reflector and a CCD camera, a single-laser-shot intensity pattern from a large angular range (theta from 90 degrees to 168 degrees and phi from 0 degrees to 360 degrees) was detected from a single aerosol (e.g., a Bacillus subtilisspore, a 1-microm-diameter polystyrene latex sphere, or a cluster of either of these) flowing through the reflectors focal volume at 5 m/s. Noticeable difference in the large-angle-range two-dimensional angular optical scattering (LATAOS) suggest that the LATAOS pattern could be useful in differentiating and classifying life-threatening aerosols from normal background aerosols.     

Catalytic alcoholysis of tetramethylsilane via Pt-mediated C-H bond activation

Tetramethylsilane reacts with 2,2,2-trifluoroethanol (TFE) in the presence of a cationic platinum(II) catalyst [(NN)PtMe(TFE)]+ (NN = 1,2-bis(3,5-dimethylphenylimino)butane). Catalytic Si-C bond heterolysis results in the formation of the trimethylsilyl ether, Me3SiOCH2CF3, accompanied by liberation of one equivalent of methane. Preliminary experiments suggest that a rate-determining C-H bond activation precedes rapid attack by solvent at silicon to yield the silyl ether product and regenerate the active platinum methyl cation.     

Trapping specific quaternary states of the allosteric enzyme aspartate transcarbamoylase in silica matrix sol-gels

The extreme T and R quaternary structures of the allosteric enzyme aspartate transcarbamoylase have been trapped by encapsulation in a silica sol-gel matrix. Detection of the specific quaternary structure present in the sol-gel was accomplished using a pyrene-labeled version of the enzyme that exhibited monomer fluorescence in the T quaternary structure and excimer fluorescence in the R quaternary structure. Using thin films of the encapsulated enzyme, kinetics of the T and R states could be determined without interconversion of the states. Using a monolith form of the encapsulated enzyme, the transition from the T or the R structure was monitored. Within the sol-gel matrix, the rate of the transition was slowed approximately 105 over that observed in solution.     

A three-curves theorem for viscosity subsolutions of parabolic equations

We prove a three-curves theorem for viscosity subsolutions of fully nonlinear uniformly parabolic equations .

     

A Note on Q-order of Convergence

To complement the property of Q-order of convergence we introduce the notions of Q-superorder and Q-suborder of convergence. A new definition of exact Q-order of convergence given in this note generalizes one given by Potra. The definitions of exact Q-superorder and exact Q-suborder of convergence are also introduced. These concepts allow the characterization of any sequence converging with Q-order (at least) 1 by showing the existence of a unique real number q [1,+] such that either exact Q-order, exact Q-superorder, or exact Q-suborder q of convergence holds.This revised version was published online in October 2005 with corrections to the Cover Date.     

Stochastic processes with sample paths in reproducing kernel Hilbert spaces

A theorem of M. F. Driscoll says that, under certain restrictions, the probability that a given Gaussian process has its sample paths almost surely in a given reproducing kernel Hilbert space (RKHS) is either or . Driscoll also found a necessary and sufficient condition for that probability to be .

Doing away with Driscoll's restrictions, R. Fortet generalized his condition and named it nuclear dominance. He stated a theorem claiming nuclear dominance to be necessary and sufficient for the existence of a process (not necessarily Gaussian) having its sample paths in a given RKHS. This theorem - specifically the necessity of the condition - turns out to be incorrect, as we will show via counterexamples. On the other hand, a weaker sufficient condition is available.

Using Fortet's tools along with some new ones, we correct Fortet's theorem and then find the generalization of Driscoll's result. The key idea is that of a random element in a RKHS whose values are sample paths of a stochastic process. As in Fortet's work, we make almost no assumptions about the reproducing kernels we use, and we demonstrate the extent to which one may dispense with the Gaussian assumption.