Strings with dimension-dependent intercept

By changing the boundary conditions of the relativistics string in extra dimensions, the intercept α(0) is lowered to $\text{1 ?}\text{1}\text{16}\text{(26 ?D}{}_0\text{)}$ in the modified orbital model, where D₀ is the dimensionality of the Poincaré-invariant subspace of space-time. In the modified model of the spinning string, the boson intercept becomes $\text{1}\text{2}\text{?}\text{1}\text{8}\text{(10 ? D}{}_{\mathrm{o}}\text{)}$, while the fermion intercept stays at zero. The projective invariance of the ground state is broken, giving the “photon” mass by a Higgs-like mechanism. Unfortunately, the strings have a negative “G parity”, so the usual, unshifted strings appear as intermediate states in the scattering amplitudes. Also, some of the amplitudes are not dual.     

Compactness in fuzzy topological spaces

Since earlier approaches to compactness in fuzzy spaces have serious limitations, we propose a new definition of fuzzy space compactness. In doing so, we observe that it is possible to have degrees of compactness, which we call α-compactness (α a member of a designated lattice). We obtain a Tychonoff Theorem for an arbitrary product of α-compact fuzzy spaces and a 1-point compactification. We prove that the fuzzy unit interval is α-compact.     

Characterization of pure high-grade DCIS on magnetic resonance imaging using the evolving breast MR lexicon terminology: can it be differentiated from pure invasive disease?

Magnetic resonance imaging (MRI) is now a recognized method of imaging the breast. Unfortunately, there is lack of standardization in the MRI terminology used to characterize the appearance of breast lesions. Moreover, cases of mixed histologies are often imaged. We retrospectively identified cases of pure high-grade ductal carcinoma in situ (DCIS) using the recently introduced breast MRI lexicon and characterized the lesions in order to try and identify features that might distinguish high-grade DCIS from invasive disease. Five-year review of our institution's database revealed 637 patients underwent gadolinium-enhanced breast MRI examination. Twenty patients had histologically proven pure high-grade DCIS. After excluding patients with previous chemotherapy or inadequate MRI examination, 13 patients were analyzed and compared to the 13 most recent cases of pure invasive breast carcinoma. The morphological and dynamic features were then compared. High-grade DCIS cases were significantly more likely to show focal branching pattern (P=.03) and to have an irregular contour (P=.03), compared with invasive disease. Although of marginal statistical significance, DCIS lesions are more likely to have a lower morphological score than invasive carcinoma (P=.06), whilst the latter is more likely to show ring enhancement (P=.07). Use of breast MRI for staging at our institution shows that pure DCIS and pure invasive cancers are both rare entities. Despite the relatively limited numbers, we identified features that would help to differentiate high-grade DCIS from invasive carcinoma on MRI.     

Structural anisotropy and internal magnetic fields in trabecular bone: coupling solution and solid dipolar interactions

We investigate the use of intermolecular multiple-quantum coherence to probe structural anisotropy in trabecular bone. Despite the low volume fraction of bone, the bone-water interface produces internal magnetic field gradients which modulate the dipolar field, depending on sample orientation, choice of dipolar correlation length, correlation gradient direction, and evolution time. For this system, the probing of internal magnetic field gradients in the liquid phase permits indirect measurements of the solid phase dipolar field. Our results suggest that measurements of volume-averaged signal intensity as a function of gradient strength and three orthogonal directions could be used to non-invasively measure the orientation of structures inside a sample or their degree of anisotropy. The system is modeled as having two phases, solid and liquid (bone and water), which differ in their magnetization density and magnetic susceptibility. A simple calculation using a priori knowledge of the material geometry and distribution of internal magnetic fields verifies the experimental measurements as a function of gradient strength, direction, and sample orientation.     

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.     

Multipliers of spherical harmonics and energy of measures on the sphere

We consider the operator,f(Δ) for Δ the Laplacian, on spaces of measures on the sphere inR ^d , show how to determine a family of approximating kernels for this operator assuming that certain technical conditions are satisfied, and give estimates for theL²-norm off(Δ)μ in terms of the energy of the measure μ. We derive a formula, analogous to the classical formula relating the energy of a measure onR ^d with its Fourier transform, comparing the energy of a measure on the sphere with the size of its spherical harmonics. An application is given to pluriharmonic measures.     

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.