2-microlocal analysis of martingales and stochastic integrals

Recently, a new approach in the fine analysis of sample paths of stochastic processes has been developed to predict the evolution of the local regularity under (pseudo-)differential operators. In this paper, we study the sample paths of continuous martingales and stochastic integrals. We proved that the almost sure 2-microlocal frontier of a martingale can be obtained through the local regularity of its quadratic variation. It allows to link the Hölder regularity of a stochastic integral to the regularity of the integrand and integrator processes. These results provide a methodology to predict the local regularity of diffusions from the fine analysis of its coefficients. We illustrate our work with examples of martingales with unusual complex regularity behaviour and square of Bessel processes.     

Measurements of velocity distributions in the deformation zone in cold rolling by a scanning LDV

Experimental determination of the velocity distribution in the deformation zone is of significant importance to investigate the metal flow in both conventional and asymmetrical rolling processes. In this paper, a scanning laser Doppler velocimetry (LDV) system, designed for measuring the velocity distributions in the deformation zone in plate rolling is reported. The LDV used for the rolling process is briefly described and then the scanning mechanism based on beam displacement by a rotating transparent plate is introduced. The relationship among the scanning distance, the beam-cross angle of the LDV system and the rotating angle of the plate is established. The scanning LDV was first tested with a rotating disk and then applied in the rolling process. The test results have demonstrated the feasibility of the scanning LDV.     

Structure determination of slowly exchanging conformers in solution using high‐resolution NMR,computational modeling and DFT‐GIAO chemical shielding: application to an erythronolide A derivative

We discuss and demonstrate the potential of HSQC‐TOCSY and HSQC‐NOESY experiments to offer solutions for overlap problems in COSY and NOESY spectra, leading to improved signals that can be unambiguously assigned to individual carbons. Direct comparison of experimental ¹H and ¹³C chemical shielding with density functional theory (DFT)‐calculated values are uninformative; in contrast, the relative differences in experimental shielding between pairs of molecules correlates well with the relative differences in DFT‐GIAO shielding for the computed lowest energy conformers. A detailed application of both experimental and theoretical techniques is illustrated for slowly exchanging conformers of an erythronolide A derivative, which demonstrates that structure determination can strongly benefit from the interplay between experiment and theory. Copyright © 2009 John Wiley & Sons, Ltd.     

One-pot synthesis of new 6-(alkylamine)dibenzo[c,e][1,2]oxaphosphinine-6-oxides

Several new 6-(alkylamine)-6H-dibenz[c,e][1,2]oxaphosphinine-6-oxides were prepared through a one-pot reaction, starting with 2-phenylphenol, phosphorus trichloride, and a Zn catalyst, to form 6-chloro-6H-dibenz[c,e][1,2]oxaphosphine. The alkylamine derivatives were subsequently prepared through a nucleophilic substitution reaction involving aliphatic amines and H₂O₂ oxidation under soft conditions. This method has the advantages that it is a one-pot synthesis, does not require an inert atmosphere, and involves in situ catalyst formation.     

Synthesis, photophysical and electrophosphorescent properties of fluorene-based platinum(II) complexes

A series of platinum(II) complexes bearing tridentate cyclometalated C^N^N (C^N^N=6-phenyl-2,2'-bipyridine and π-extended R-C^N^N=3-[6'-(naphthalen-2'-yl)pyridin-2'-yl]isoquinoline) ligands with fluorene units have been synthesised and their photophysical properties have been studied. The fluorene units are incorporated into the cyclometalated ligands by a Suzuki coupling reaction. An increase in the π-conjugation of the cyclometalated ligands confers favourable photophysical properties compared to the 6-phenyl-2,2'-bipyridine analogues. The fluorene-based platinum(II) complexes display vibronic-structured emission bands with λ(max)=558-601 nm, and high emission quantum yields up to 0.76 in degassed dichloromethane. Their emissions are tentatively assigned to excited states with mixed (3)IL/(3)MLCT parentage (IL=intraligand, MLCT=metal-to-ligand charge transfer). The crystal structures of these platinum(II) complexes reveal extensive Pt(II)···π and/or π-π interactions. The fluorene-based platinum(II) complexes are soluble in organic solvents, have high thermal stability with decomposition temperature >350 °C, and can be thermally vacuum-sublimed or solution-processed as phosphorescent dopants for the fabrication of organic light-emitting diodes (OLEDs). A monochromic OLED with 3d as dopant (2 wt%) fabricated by vacuum deposition gave a current efficiency of 14.7 cd A(-1) and maximum brightness of 27000 cd m(-2). A high current efficiency (9.2 cd A(-1)) has been achieved in a solution-processed OLED using complex 3f (5 wt%) doped in a PVK (poly(9-vinylcarbazole)) host.