The prospects for high resolution optical brain imaging: the magnetic resonance perspective

Various analogs of NMR and MRI are now technically possible in optics; specifically, high-resolution laser-pulse shaping and complex pulse sequence generation with well-defined phase shifts has been demonstrated. Here we summarize this technology and discuss the potential for these methods to enhance optical functional imaging, competing with (and surpassing?) what is possible by functional MRI.     

Aerosol assisted chemical vapour deposition of tungsten oxide films from polyoxotungstate precursors: active photocatalysts

Aerosol assisted chemical vapour deposition of polyoxotungstate precursors [n-Bu4N]2[W6O19] and [n-Bu4N]4H3[PW11O39] produces films of WO(3 - x) and WO3 on glass substrates; the WO3 films show significant photocatalytic decomposition of a test organic pollutant--stearic acid--when irradiated with either 254 or 365 nm radiation.     

Isobutene polymerization using a chelating diborane co-initiator

Lewis acidic diborane 1 (J. Am. Chem. Soc. 1999, 121, 3244-3245) is highly effective for both proton- and cationogen-initiated isobutene polymerization in hydrocarbon media at low temperature. Reactions of diborane 1 with cumyl chloride and cumyl methyl ether were studied by variable-temperature 1H and 19F NMR spectroscopy. At low temperatures stable ion pairs 2a and 2b are formed; at higher temperatures these ion-pairs form phenyl-1,3,3-trimethylindan (3) with concomitant release of HCl to form 1 in the case of 2a or degradation of the anion (2b). Reaction between Ph3C-Cl and diborane 1 resulted in the generation of an ion-pair 4 consisting of the Ph3C cation very weakly associated with the chelated, mu-Cl counteranion as revealed by X-ray crystallography.     

Quadrature spectral interferometric detection and pulse shaping

We introduce a new variant of spectral interferometry, using spectrally dispersed ultrafast laser pulses and quadrature detection to measure optical thickness variations related to surface structure. We can resolve surface features with depths of 3 mm to 25 nm, using a lateral resolution of ~100mum . Quadrature detection gives a larger dynamic range and solves the sign ambiguity problem. This method has potential applications in device manufacture, optical communications, and error compensation in pulse shaping.     

Functional magnetic resonance imaging with intermolecular multiple-quantum coherences

For the first time, we demonstrate here functional magnetic resonance imaging (fMRI) using intermolecular multiple-quantum coherences (iMQCs). iMQCs are normally not observed in liquid-state NMR because dipolar interactions between spins average to zero. If the magnetic isotropy of the sample is broken through the use of magnetic field gradients, dipolar couplings can reappear, and hence iMQCs can be observed. Conventional (BOLD) fMRI measures susceptibility variations averaged over each voxel. In the experiment performed here, the sensitivity of iMQCs to frequency variations over mesoscopic and well-defined distances is exploited. We show that iMQC contrast is qualitatively and quantitatively different from BOLD contrast in a visual stimulation task. While the number of activated pixels is smaller in iMQC contrast, the intensity change in some pixels exceeds that of BOLD contrast severalfold.     

Explicit gradient estimates for minimal Lagrangian surfaces of dimension two

We derive explicit, uniform, a priori interior Hessian and gradient estimates for special Lagrangian equations of all phases in dimension two. Y. Yuan is partially supported by an NSF grant.     

Separable subspaces of affine function spaces on convex compact sets

Let K be a compact convex subset of a separated locally convex space (over R) and let Ap(K) denote the space of all continuous real-valued affine mappings defined on K, endowed with the topology of pointwise convergence on the extreme points of K. In this paper we shall examine some topological properties of Ap(K). For example, we shall consider when Ap(K) is monolithic and when separable compact subsets of Ap(K) are metrizable.     

Bézout rings with almost stable range 1

Elementary divisor domains were defined by Kaplansky [I. Kaplansky, Elementary divisors and modules, Trans. Amer. Math. Soc. 66 (1949) 464-491] and generalized to rings with zero-divisors by Gillman and Henriksen [L. Gillman, M. Henriksen, Some remarks about elementary divisor rings, Trans. Amer. Math. Soc. 82 (1956) 362-365]. In [M.D. Larsen, W.J. Lewis, T.S. Shores, Elementary divisor rings and finitely presented modules, Trans. Amer. Math. Soc. 187 (1) (1974) 231-248], it was also proved that if a Hermite ring satisfies (N), then it is an elementary divisor ring. The aim of this article is to generalize this result (as well as others) to a much wider class of rings. Our main result is that Bézout rings whose proper homomorphic images all have stable range 1 (in particular, neat rings) are elementary divisor rings.