The Furuta inequality in Banach -algebras

Let be real numbers with and Furuta (1987) proved that if bounded linear operators on a Hilbert space satisfy , then . This inequality is called the Furuta inequality and has many applications. In this paper, we prove that the Furuta inequality holds in a unital hermitian Banach -algebra with continuous involution.

     

Superconductivity and crystallographic properties of La2 − xMxCuO4 − δ (M = Na, K)

Superconductivity and crystallographic properties of La_{2 − x}M_xCuO_{4 − δ} (M = Na, K) are studied. In the La_{2 − x}M_xCuO_{4 − δ} system, superconductivity is detected for x 0.2. Oxygen content analysis shows that the system has more oxygen vacancies than the La_{2 − x}Sr_xCuO_{4 − δ} system. These oxygen vacancies may reduce the hole concentration, and high Na-doping is needed to produce superconductivity. In the La_{2 − x}K_xCuO_{4 − δ} system, superconductivity is observed for the first time. Resistivity and magnetic susceptibility measurements show that T_c(onset) is 40 K and the Meissner volume fraction is about 4% for x = 0.7. The system changes from orthorhombic to a tetragonal K₂NiF₄ structure at x ≈ 0.3 and only tetragonal samples show superconductivity.     

Magnetic circular dichroism study of directly fused porphyrins.

The magnetic circular dichroism (MCD) spectra of doubly and triply linked fused bisporphyrins (2MD and 2MT, M = Ni, Zn, Cu, Pd, and H2) and triply linked higher oligomers (3ZnT and 4ZnT) have been measured, and their Q-bands assigned based on the results of INDO/s calculations. In contrast to the Faraday A term observed for the Q(0,0) band of Ni(II) tetraphenylporphyrin, a single positive Faraday B term was observed for the lowest energy transition of the fused systems. The calculations indicated that the molecular orbitals (MOs) of the directly fused porphyrins consist of linear combinations of the constituent monomeric MOs, and that the effect of lowering the symmetry is always larger on the lowest unoccupied molecular orbital (LUMO) than on the highest occupied molecular orbital (HOMO). On the basis of Michl's perimeter model, these features can be correlated with the observed positive MCD signs in the near infrared region. A weak absorption band at 600-700 nm for the fused dimers can be assigned to a short-axis polarized Q transition.     

Molecular orientation and mechanical anisotropy of polypropylene sheet containing N,N′‐dicyclohexyl‐2,6‐naphthalenedicarboxamide

Effect of mixing and processing conditions at T‐die extrusion on the structure and mechanical properties is studied for isotactic polypropylene (PP) containing a small amount of β‐form nucleating agent, N,N′‐dicyclohexyl‐2,6‐naphthalenedicarboxamide. It is found that trigonal β crystals are predominantly formed in the extruded samples containing the nucleating agent irrespective of the mixing and processing conditions, leading to the marked mechanical toughness. On the contrary, the molecular orientation is significantly affected by the mixing and processing conditions. In particular, it should be noted that PP molecules in the extruded sheet which was mixed at high temperature (260 °C) and extruded at low temperature (200 °C) orient perpendicular to the applied flow direction. As a result, the sheet shows anomalous mechanical anisotropy. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 424–433, 2009     

Vernodalidimers A and B, novel orthoester elemanolide dimers from seeds of Vernonia anthelmintica

Two novel elemanolide dimers, vernodalidimers A (1) and B (2), possessing a rare tricyclic ortho ester moiety, were isolated from the seeds of Vernonia anthelmintica. Their structures were elucidated by 1D and 2D NMR data and CD spectra. Vernodalidimers A (1) and B (2) exhibited potent cell growth inhibitory activity against HL-60 cells (IC₅₀ 0.72 and 0.47 μM, respectively).     

Homoleptic Zincate‐Promoted Room‐Temperature Halogen–Metal Exchange of Bromopyridines

Homoleptic lithium tri‐ and tetraalkyl zincates were reacted with a set of bromopyridines. Efficient and chemoselective bromine–metal exchanges were realized at room temperature with a substoichiometric amount of nBu₄ZnLi₂?TMEDA reagent (1/3 equiv; TMEDA=N,N,N′,N′‐tetramethylethylenediamine). This reactivity contrasted with that of tBu₄ZnLi₂?TMEDA, which was inefficient below one equivalent. DFT calculations allowed us to rationalize the formation of N???Li stabilized polypyridyl zincates in the reaction. The one‐pot difunctionalization of dibromopyridines was also realized using the reagent stoichiometrically. The direct creation of C? Zn bonds in bromopyridines enabled us to perform efficient Negishi‐type cross‐couplings.