Birational rigidity of complete intersections

We prove that every smooth complete intersection \(X=X_{d_{1}, \ldots , d_{s}}\subset \mathbb {P}^{\sum _{i=1}^{s}d_{i}}\) defined by s hypersurfaces of degree \(d_{1}, \ldots , d_{s}\) is birationally superrigid if \(5s +1\le \frac{2(\sum _{i=1}^{s}d_{i}+1)}{\sqrt{\prod _{i=1}^{s}d_{i}}}\). In particular, X is non-rational and \({{\mathrm{Bir}}}(X)={{\mathrm{Aut}}}(X)\). We also prove birational superrigidity of singular complete intersections with similar numerical condition. These extend the results proved by Tommaso de Fernex.     

Photocatalytic oxidation of propylene with molecular oxygen over highly dispersed titanium, vanadium, and chromium oxides on silica

Photocatalytic oxidation of propylene with molecular oxygen at room temperature was investigated over various silica-supported metal oxides with low loading. The photocatalytic active site is assumed to be the isolated tetrahedrally coordinated metal oxides in the ligand-to-metal charge-transferred state, such as (Mdelta- -OLdelta+). Photocatalytic epoxidation of propylene into propylene oxide was promoted over silica-supported V and Ti oxides at steady state. Over silica-supported Cr oxide, the propylene oxide formation rate was remarkably decreased with the time course in the reaction. The oxidation state and the coordination environment of the supported Ti, V, and Cr oxide species were determined by diffuse reflectance UV-vis spectroscopy (DRS) and electron spin resonance (ESR). During the photocatalytic oxidation, the oxidation state of the Ti4+ species was not varied. On the other hand, the V5+ species was partially reduced to V4+ and the Cr6+ species was successively reduced to Cr5+ and Cr3+. An isotopic tracer study of the C3H6-18O2 reaction suggests the difference of the active oxygen species between TiO2/SiO2 and V2O5/SiO2. The active oxygen species on TiO2/SiO2 is derived from molecular oxygen. On the other hand, the photogenerated products on V2O5/SiO2 incorporate the lattice oxygen of the surface metal oxide species. It is suggested that the kinds of terminal ligand (hydroxyl or oxo) of the tetrahedrally coordinated metal oxides on silica decide the active oxygen species in the photocatalytic oxidation. A photoinduced hole center on the monohydroxyl (SiO)3Ti-OH species activates molecular oxygen that reacts with propylene. In the case of the monooxo (SiO)3V=O and dioxo (SiO)2Cr=O2 species, the photoactivated lattice oxygen (OL-) directly reacts with propylene.     

Synthesis of Diblock Copolymers With Cellulose Derivatives. 2. Characterization and Thermal Properties of Cellulose Triacetate-Block-Oligoamide-15

Well-defined A-block-B type cellulose derivatives consisting of cellulose triacetate (CTA) and oligoamide-15 were synthesized. Chemical structures of the diblock copolymers were characterized by MALDI-TOF MS, ¹H-NMR, and GPC. Influence of length of CTA and oligoamide-15 segments on their thermal properties was investigated by means of differential scanning calorimetry (DSC). All diblock copolymers displayed T _g, T _c, and T _m transition temperatures. Their T _g and T _m values increased with the increase of molecular weight of CTA segment. The crystallinity of diblock copolymers increased after isothermal crystallization at 200 °C. Its X-ray analysis revealed that the diblock copolymer had CTA II crystal structure. Thermal analysis supported microphase separation between CTA and oligoamide-15 segments at room temperature, because T _g and T _m values of polyamide-15 are −7 °C and 170–180 °C, respectively.     

N-fused pentaphyrins and their rhodium complexes: oxidation-induced rhodium rearrangement

meso-Aryl-substituted pentaphyrins were isolated in the modified Rothemund-Lindsey porphyrin synthesis as a 22-pi-electron N-fused pentaphyrin ([22]NFP5) and a 24-pi-electron N-fused pentaphyrin ([24]NFP5), which were reversibly interconvertible by means of two-electron reduction with NaBH4 or two-electron oxidation with dichlorodicyanobenzoquinone (DDQ). Judging from 1H NMR data, [22]NFP5 is aromatic and possesses a diatropic ring current, while [24]NFP5 exhibits partial anti-aromatic character. Metalation of [22]NFP5 1 with a rhodium(I) salt led to isolation of rhodium complexes 9 and 10, whose structures were unambiguously characterized by X-ray diffraction analyses and were assigned as conjugated 24-pi and 22-pi electronic systems, respectively. In the rhodium(I) metalation of 1, the complex 9 was a major product at 20 degrees C, but the complex 10 became preferential at 55 degrees C. Upon treatment with DDQ, compound 9 was converted to 10 with an unprecedented rearrangement of the rhodium atom.