On the index of a holomorphic vector field tangent to a singular variety

In this article we define and compute an index for a holomorphic vector field on a (possibly singular) subvariety of a complex manifold, provided the subvariety is a local complete intersection. This index reduces to the usual Poincaré-Hopf index in case the subvariety is smooth, and is equal more generally to the index defined in [GSV] and [SS].     

Lock-exchange flows in inclined pipes: the relevance of the Prandtl mixing length model

We examine the applicability of the Prandtl mixing length model to transverse momentum and mass flux in strongly confined, stably stratified turbulent shear flows. These fluxes were measured in the vertical diametral plane of lock-exchange flows in an inclined pipe by the simultaneous use of planar laser-induced fluorescence and particle image velocimetry at local Reynolds numbers ranging from Re = 580 to 1770 and Richardson numbers ranging from Ri = 0.26 and 1.6. Measurements indicate that the eddy diffusivities of mass and momentum are symmetric about the pipe axis, with their maximum at the axis. The corresponding Prandtl mixing lengths decrease with increasing distance from the pipe axis within the central 60% of the pipe cross-section. Within the range of experimental conditions, the mixing lengths at the axis increase linearly with Ri so that the corresponding turbulent Prandtl number Pr_t decreases with Ri. In contrast, Pr_t and the mixing lengths do not display a systematic dependence on Re. Comparison with unbounded and semi-bound shear flows suggests that the strong confinement imposed by the pipe wall may be constraining the integral length scale and Prandtl mixing lengths.     

Fibrous and helical calcite crystals induced by synthetic polypeptides containing o-phospho-L-serine and o-phospho-L-threonine

The modification of CaCO(3) crystal growth by synthetic L-Ser(PO(3)H(2)) and L-Thr(PO(3)H(2)) containing polypeptides is described. The amino acids Gly, L-Glu, L-Asp, L-Ser, L-Ala, and L-Lys induced rhombohedral calcite with a rough surface. Dipeptides, Xaa-L-Ser(PO(3)H(2)) (Xaa = Gly, L-Glu, L-Asp, L-Ser, L-Ala and L-Lys) induced vaterite crystals in the lower [Ca(2+)]. On the other hand, L-Ser(PO(3)H(2))-containing polypeptides formed spherical vaterite and fibrous calcite. The characteristic helical calcite was found in the presence of copoly[L-Ser(PO(3)H(2))(75)L-Asp(25)] or poly[L-Ser(PO(3)H(2))(3)-L-Asp]. Fibrous calcite, spherical vaterite, and helical calcite crystals were subjected to XRD and EDX analysis. XRD revealed the specific faces of these crystals. EDX spectra and surface analysis visualized the localization of the polypeptides and CaCO(3) components. Together with TEM and SAED data, we propose hypothetical growth mechanisms for the fibrous and helical calcite crystals.     

Nanoparticle plasmon-assisted two-photon polymerization induced by incoherent excitation source

We demonstrate the possibility to achieve optical triggering of photochemical reactions via two-photon absorption using incoherent light sources. This is accomplished by the use of arrays of gold nanoparticles, specially tailored with high precision to obtain high near-field intensity enhancement.     

Aerobic oxidative kinetic resolution of racemic alcohols with bidentate ligand-binding Ru(salen) complex as catalyst

Chiral Ru(salen)(nitrosyl) complex 1 is a useful catalyst for asymmetric aerobic oxidation of alcohols under photo-irradiation. In this study, it was found that addition of β-hydroxy ketone or 1,3-diketone had a significant influence on its asymmetric catalysis. For example, the addition of 1,3-bis(p-bromophenyl)propane-1,3-dione 9 improved the relative reaction ratio in kinetic resolution of simple racemic secondary alcohols up to 30, while the addition gave an adverse effect on desymmetrization of an acyclic meso-1,3-diol. This additive effect was considered to be attributable to the chelate formation of the β-hydroxy ketone or 1,3-diketone with a Ru(salen) complex.     

Photoisomerization and thermal isomerization of arylazoimidazoles

Photoisomerization and thermal isomerization behaviors of an extensive series of arylazoimidazoles are investigated. Absorption spectra are characterized by a structured pipi* absorption band around 330-400 nm with a tail on the lower energy side extending to 500 nm corresponding to an npi* transition. The trans-to-cis photoisomerization occurs on excitation into these absorption bands. The quantum yields are dependent on the excitation wavelength, as observed for azobenzene derivatives, but are generally larger than those of azobenzene. The thermal cis-to-trans isomerization rates are also generally larger than that of azobenzene and are comparable to those of 4-N,N-dimethylaminoazobenzene and 4-nitroazobenzene. Arylazoimidazoles with no substituent on the imidazole nitrogen are unique in that the quantum yield for the trans-to-cis photoisomerization and the rate of thermal cis-to-trans isomerization are particularly large. It is proposed that the fast thermal isomerization is due to an involvement of self-catalyzed and protic molecule-assisted tautomerization to a hydrazone form.