On a new construction of geometric mean of -operators

For n positive definite operators A₁,…,A_n, Ando-Li-Mathias defined geometric mean of n-operators by symmetric procedure. It has many nice properties, and is studied by many authors. But the process is so complicated to compute. In this paper, we shall attempt to make a new construction of geometric mean of n-operators which we can compute it easier than geometric mean by Ando–Li–Mathias.     

Polyaniline–DNA microsphere formation by simple electropolymerization

Polyaniline (PANI) microspheres were prepared by electrochemical polymerization. To obtain PANI having novel micro- and nanostructures, by the potential scan technique, aniline was electropolymerized in the presence of DNA using four polymerizing solutions containing different acids: H₂SO₄, C₆H₅SO₃H, HClO₄, and CF₃COOH. The growth rate of the PANI film on the electrode surface decreased by the presence of DNA, suggesting that DNA interacted with the growing PANI molecules during the electropolymerization. The growth rate also depended on the type of acid, i.e., the anion, in the polymerizing solution and was in the order of SO₄ ²⁻ > C₆H₅SO₃ ⁻ > ClO₄ ⁻ > CF₃COO⁻, which significantly coincided with the reverse order of the Hofmeister series representing the lyophilicity of the anion. When aniline was electropolymerized in the CF₃COOH polymerizing solution containing DNA, PANI microspheres were obtained without any templates. This PANI showed a sufficient redox activity in the less acidic solution in which the ordinary PANI has a slight redox activity. On the other hand, the electronic state of the PANI differed from the ordinary ones; a new absorption band was evident at 620 nm. The difference in the redox activity and electronic state suggested that the DNA molecules were incorporated in the PANI and electronically interacted with the PANI molecules.     

Mechanistic study on the electrochemical reduction of 9,10-anthraquinone in the presence of hydrogen-bond and proton donating additives

The electrochemical reduction of 9,10-anthraquinone (AQ) was investigated in CH(3)CN in both the absence and presence of the hydrogen-bond and proton donating additives, CH(3)OH, CH(CF(3))(2)OH, phenol, 4-methoxyphenol, 4-cyanophenol, 2,4,6-trichlorophenol, and benzoic acid (BA). Three clearly different types of electrochemical behavior were observed with increasing concentrations of the additives, and were simulated to analyze the reaction mechanisms. Type I was observed for weakly interacting additives, such as CH(3)OH, characterized by positive shifts of the two well-separated reduction waves, corresponding to the formation of AQ(?-) and AQ(2-), with no loss of reversibility. The second wave shifted more strongly, and finally merged with the first. These behaviors are explained by the association of AQ(2-) with the additives via strong hydrogen-bonding. Type II is attributed to a reduction mechanism involving quantitative formation of strong hydrogen-bonded complexes of AQ(2-) with additives, such as CH(CF(3))(2)OH, phenol and 4-methoxyphenol, showing a reversible or quasireversible two-electron reduction wave with increasing concentrations of the additives. The behavior of Type III, observed in the presence of strongly interacting additives, such as 2,4,6-trichlorophenol and BA, is characterized by a voltammogram composed of the 2-electorn cathodic and the broad anodic waves without keeping reversibility, facilitated by proton transfer in the hydrogen-bonded complexes, AQ(?-)-BA and AQ(2-)-BA. The effects of hydrogen-bonding and protonation on the electrochemistry of AQ have been systematically demonstrated in terms of the potentials and reaction pathways of the various species, which appear in quinone-hydroquinone systems.     

Novel syntheses and properties of meso-tetraaryl-octabromo-tetranaphtho[2,3]porphyrins (Ar4Br8TNPs)

o-Quinodimethane (o-QDM) generated from benzosultine was used to extend the pyrrole system for the preparation of octabromo-tetranaphtho[2,3]porphyrins via oxidative aromatization. The properties of these bromoporphyrins were presented and chemical transformation via Pd-catalyzed Suzuki reaction was also effectively achieved.     

π-Fused bis-BODIPY as a candidate for NIR dyes

Benzene-fused bis-(borondipyrromethene)s (bis-BODIPYs) were synthesized by retro-Diels-Alder reaction of the corresponding bicyclo[2.2.2]octadiene-fused (BCOD-fused) bis-BODIPYs, which were, in turn, prepared from 4,8-ethano-4,8-dihydropyrrolo[3,4-f]isoindole derivatives. The π-fused bis-BODIPY chromophores were designed to show intensive absorption and strong fluorescence in the near-infrared region and not to have any strong absorption in the visible region. A 6,10-dibora-5a,6a,9a,10a-tetraaza-s-indaceno[2,3-b:6,5-b']difluorene derivative (syn-bis-benzoBODIPY) obtained by a thermal retro-Diels-Alder reaction of the corresponding BCOD-fused BODIPY dimer has strong absorption and emission bands at 775 and 781 nm, respectively. The absolute quantum yield is 0.36. The absorption is more than 5.0 times stronger than other absorptions observed in the visible region. In the case of 6,15-dibora-5a,6a,14a,15a-tetraaza-s-indaceno[2,3-b:6,7-b']difluorene derivatives (anti-bis-benzoBODIPY), the absorption and emission maxima exceed 840 nm.     

Total synthesis of ent-calystegine B4 via nitro-Michael/aldol reaction

Optically active ent-calystegine B4 was prepared in 13 steps from commercially available chiral L-dimethyl tartrate. The synthesis was achieved by the Michael addition and the aldol reaction of nitromethane to form cycloheptanone in a stereoselective manner. Reduction of the nitro group in the presence of Boc(2)O accomplished an efficient conversion to amino cycloheptanone, which readily afforded the desired ent-calystegine B4.     

Confusion of Möbius aromaticity: disruption of annulenic pathway in singly N-confused [28]hexaphyrin and its mono-Pd(II) complex

Singly N-confused [26] and [28]hexaphyrins (4, 5) with planar and twisted structures, respectively, were prepared via the acid catalyzed [3 + 3] condensation of N-confused and regular tripyrrane precursors. Hückel aromaticity is observed for [26]hexaphyrin, while the [28]hexaphyrin and its mono-Pd(II) complex exhibit "nonaromaticity" in spite of their M?bius-type structures, judging from the spectroscopic features and theoretical calculations.     

Scale-model experiments of moving fire whirl over a line fire

A fire whirl, observed during a wildland fire in Brazil in 2010, occurred over a narrow but long line fire and moved along the line fire at nearly a constant speed. There appeared to be no mountains, tall buildings or trees near the scene, indicating that the fire whirl was generated merely by the interaction between the line fire and background wind. Scale-model experiments having different line fire configurations were designed and performed to reconstruct the above-mentioned Brazil fire whirl. Moving fire whirls were successfully reconstructed during the scale-model experiments, the mechanism and conditions of which are discussed herein.     

Novel one-pot synthesis of 5-alkenyl-15-alkynylporphyrins and their derivatisation to a butadiyne-linked benzoporphyrin dimer

5-Alkenyl-15-alkynylporphyrins have been obtained unexpectedly by [2 + 2] acid-catalyzed condensation of dipyrrylmethane and TMS propynal in addition to 5,15-dialkynylporphyrin, and the unsymmetrical porphyrin can be converted to a butadiyne-linked dimer by selective desilylation of the alkynyl TMS.