Trace inequalities for products of matrices

In this short paper, we study some trace inequalities of the products of the matrices and the power of matrices by the use of elementary calculations.     

Sigmatropic Rearrangements of Hypervalent‐Iodine‐Tethered Intermediates for the Synthesis of Biaryls

Metal‐free dehydrogenative couplings of aryliodanes with phenols to afford 2‐hydroxy‐2′‐iodobiaryls have been developed. This reaction proceeds through ligand exchange on the hypervalent iodine atom followed by a [3,3] sigmatropic rearrangement and with complete regioselectivity. This coupling, in combination with in situ oxidation by mCPBA, enables the convenient conversion of iodoarenes into desirable biaryls. The obtained biaryls have convertible iodo and hydroxy groups in close proximity, and are thus synthetically useful, as exemplified by the controlled syntheses of π‐extended furans and a substituted [5]helicene. DFT calculations clearly revealed that the rearrangement is sigmatropic, with C?C bond formation and I?O bond cleavage proceeding in a concerted manner. Acetic acid, which was found to be the best solvent for this protocol, renders the iodine atom more cationic and thus accelerates the sigmatropic rearrangement.     

Local electrostatic field induced by the carotenoid bound to the reaction center of the purple photosynthetic bacterium Rhodobacter sphaeroides

Electroabsorption (EA) spectra were recorded in the region of the reaction center (RC) Qy absorption bands of bacteriochlorophyll (Bchl) and bacteriopheophytin, to investigate the effect of carotenoid (Car) on the electrostatic environment of the RCs of the purple bacterium Rhodobacter (Rb.) sphaeroides. Two different RCs were prepared from Rb. sphaeroides strain R26.1 (R26.1-RC); R26.1 RC lacking Car and a reconstituted RC (R26.1-RC+ Car) prepared by incorporating a synthetic Car (3,4-dihydrospheroidene). Although there were no detectable differences between these two RCs in their near infrared (NIR) absorption spectra at 79 and 293 K, or in their EA spectra at 79 K, significant differences were detected in their EA spectra at 293 K. Three nonlinear optical parameters of each RC were determined in order to evaluate quantitatively these differences; transition dipole-moment polarizability and hyperpolarizability (D factor), the change in polarizability upon photoexcitation (Deltaalpha), and the change in dipole-moment upon photoexcitation (Deltamu). The value of D or Deltaalpha determined for each absorption band of the two RC samples showed similar values at 77 or 293 K. However, the Deltamu values of the special pair Bchls (P) and the monomer Bchls absorption bands showed significant differences between the two RCs at 293 K. X-ray crystallography of the two RCs has revealed that a single molecule of the solubilizing detergent LDAO occupies part of the carotenoid binding site in the absence of a carotenoid. The difference in the value of Deltamu therefore represents the differential effect of the detergent LDAO and the carotenoid on P. The change of electrostatic field around P induced by the presence of Car was determined to be 1.7 x 10(5) [V/cm], corresponding to a approximately 10% change in the electrostatic field around P.     

Convergent and rapid assembly of substituted 2-pyridones through formation of N-alkenyl alkynylamides followed by gold-catalyzed cycloisomerization

A new method for the convergent and rapid assembly of substituted 2-pyridones was developed through the formation of N-alkenyl alkynylamides (amide-linked 1,5-enynes) by N-acylation of imines with alkynoyl chlorides and the subsequent cationic Au(I)/PPh 3-catalyzed cycloisomerization.     

Experimental investigation of the closest parallel pulses in holographic femtosecond laser processing

In holographic femtosecond laser processing, diffractive parallel pulses are distorted by phase discontinuities and mutual interference between the neighborhoods in the reconstructed image of a Fourier computer-generated hologram when the interval is smaller than the beam diameter. We investigated holographic fabrication on a glass surface using parallel pulses with different intervals. We found the closest parallel pulses with sufficient separation to avoid mutual interference in holographic femtosecond laser processing. The minimum interval was 2.8 times larger than the diffracted beam diameter. The experimental results were also supported by a computer simulation. Our findings will be very useful in the design of holographic laser processing systems.     

Nickel Acetylacetonate-Induced 1,4-Additions of 1-Alkenyl(Disiamyl)Boranes to α,β-Unsaturated Ketones,Esters and Nitriles

The conjugate addition of 1-alkenyl(disiamyl)boranes to α,β-unsaturated ketones, esters, or nitriles was carried out in the presence of Ni(acac)₂ and triethylamine in DMF. The reactions provided γ,δ-unsaturated ketones, esters, and nitriles in high yields while retaining the original configuration of the 1-alkenylboranes. A similar addition reaction of 1-alkenyl(disiamyl)boranes to 1-acetyl-2-vinylcyclopropane produced the terminal and internal coupling products, 5,8-alkadien-2-on and 5-ethenyl-6-alken-2-on, in high yields in some cases with high regioselectivity favoring the terminal addition products.     

Mechanistic Investigation of a Synthetic Route to Biaryls by the Sigmatropic Rearrangement of Arylsulfonium Species

A comprehensive mechanistic investigation was conducted on the coupling reaction of aryl sulfoxides with phenols by using trifluoroacetic anhydride to yield biaryls. NMR experiments revealed that our previously proposed mechanism, which consists of a cascade of an interrupted Pummerer reaction and a rate-determining [3,3] sigmatropic rearrangement, is reasonable. The electronic effects of the substrates were also evaluated to elucidate the nature of the rearrangement step. Based on experimental observations and theoretical calculations, we conclude that the rearrangement is highly asynchronous and stepwise rather than concerted when electron-rich phenols are employed for the reaction.     

Array of a dye-doped polymer-based microlaser with multiwavelength emission

This Letter reports a convenient method of fabricating a polymer-based microlaser array. Laterally aligned plastic micropillars equipped with an optical resonator were fabricated by using a lithographic technique with an organic-dye-doped photopolymer, which operated as a laser element with a vertical cavity. Under optical pumping, very fine emission spectra showing a Fabry-Perot-type lasing oscillation were observed. Using this technique, integrated laser cavities with desired operation wavebands can be produced easily.     

Energy-transferred photoluminescence from thiophene/phenylene oligomer thin films

Photoluminescence (PL) based on Förster energy transfer between p-sexiphenyl (p-6P) and 5,5′-bis(4-phenylyl)-2,2′-bithiophene (BP2T) was investigated for their coevaporated and laminated thin films. In the former films, fluorescence quenching of the p-6P was accompanied by appearance of BP2T fluorescence, which indicated existence of the energy transfer between the donors and the acceptors. The latter films were fabricated by successive depositions of p-6P, MgF₂ and BP2T in which the thickness of the MgF₂ spacer was varied. The energy-transferred acceptor fluorescence was suppressed by the spacer thicker than the Förster distance (∼10 nm).     

Unconventional pairing originating from the disconnected Fermi surfaces of superconducting LaFeAsO1-xFx

For a newly discovered iron-based high T_{c} superconductor LaFeAsO1-xFx, we have constructed a minimal model, where inclusion of all five Fe d bands is found to be necessary. The random-phase approximation is applied to the model to investigate the origin of superconductivity. We conclude that the multiple spin-fluctuation modes arising from the nesting across the disconnected Fermi surfaces realize an extended s-wave pairing, while d-wave pairing can also be another candidate.