Poisson Boundary of the Dual of SU q (n)

We prove that for any non-trivial product-type action α of SU_q(n) (0<q<1) on an ITPFI factor N, the relative commutant is isomorphic to the algebra L^∞() of bounded measurable functions on the quantum flag manifold . This is equivalent to the computation of the Poisson boundary of the dual discrete quantum group . The proof relies on a connection between the Poisson integral and the Berezin transform. Our main technical result says that a sequence of Berezin transforms defined by a random walk on the dominant weights of SU(n) converges to the identity on the quantum flag manifold. Supported by JSPS. Partially supported by the Norwegian Research Council. Supported by the SUP-program of the Norwegian Research Council.     

Synthesis of 1-beta-O-acyl glucuronides of diclofenac, mefenamic acid and (S)-naproxen by the chemo-selective enzymatic removal of protecting groups from the corresponding methyl acetyl derivatives

Using a straightforward chemo-enzymatic procedure, 1-beta-O-acyl glucuronides of three non-steroidal anti-inflammatory drugs, diclofenac (DF) 5, mefenamic acid (MF) 6 and (S)-naproxen (NP) 7, were prepared. Caesium salts of these carboxylic acid drugs reacted with commercially available methyl 2,3,4-tri-O-acetyl-1-bromo-1-deoxy-alpha-D-glucopyranuronate 4 to give exclusively the corresponding 1-beta-O-acyl glucuronides 8-10 in moderate yields. The protecting acetyl (for -OH group) and methyl ester (for -CO2H group) groups of each sugar moiety were easily removed to provide the corresponding free 1-beta-O-acyl glucuronides 1-3 in high yields. Deprotection was achieved through effective enzyme-catalysed chemo-selective hydrolyses of the acetyl groups using lipase AS Amano (LAS), and of the methyl ester group using esterase from porcine liver (PLE).     

Infrared vibrational autodetachment spectroscopy of microsolvated benzonitrile radical anions

Vibrational spectra of microsolvated benzonitrile radical anions (C6H5CN- -S; S = H2O and CH3OH) were measured by probing the electron detachment efficiency in the 3 microm region, representing resonance bands of autodetachment via OH stretching vibrations of the solvent molecules. The hydrogen-bonded OH band for both the cluster anions exhibited a large shift to the lower energy side with approximately 300 cm-1 compared to those for the corresponding neutral clusters. The solvent molecules are bound collinearly to the edge of the CN group of the benzonitrile anion in the cluster structures optimized with the density functional theory, in which the simulated vibrational energies are in good agreement with the observed band positions. Natural population analyses were performed for a qualitative implication in changes of solvent orientation upon electron attachment. Asymmetric band shapes depending on the vibrational modes are discussed with respect to dynamics of the autodetachment process from a theoretical aspect incorporated with density functional calculations.     

Several types of bilayer smectic liquid crystals with ferroelectric and antiferroelectric properties in binary mixture of dimeric compounds

The mesomorphic behavior and phase structure were examined in the mixture of two kinds of dimeric compounds, alpha,omega-bis(4-alkoxyanilinebenzylidene-4'-carbonyloxy)pentane (mOAM5AMOm), by optical microscopy, X-ray diffraction, polarization switching, and second-harmonic generation measurements. One compound is 4OAM5AMO4 with a short terminal alkyl chain that forms a single-layer smectic phase (SmCAs) with a random mixing of spacer and tail groups. Another compound is 16OAM5AMO16 with a long terminal alkyl chain that forms a chiral, anticlinic, and antiferroelectric bilayer phase (SmCAb) with the bent molecules tilted to the bilayer. By mixing these two compounds, the SmCAs phase of 4OAM5AMO4 is easily destabilized, leading to the wide content region of the bilayer phases. In the bilayer regime, three other smectic phases are newly induced. Two of them are antiferroelectric and ferroelectric phases in which the molecules lie perpendicularly with respect to the layer. The other shows no polar response to an external electric field and behaves like a smectic A. The new appearance of these bilayer phases is discussed as a mixing effect of long and short tail groups.     

2d–4d connection between q-Virasoro/W block at root of unity limit and instanton partition function on ALE space

We propose and demonstrate a limiting procedure in which, starting from the q-lifted version (or K-theoretic five-dimensional version) of the (W)AGT conjecture to be assumed in this paper, the Virasoro/W block is generated in the r-th root of unity limit in q   in the 2d side, while the same limit automatically generates the projection of the five-dimensional instanton partition function onto that on the ALE space R⁴/_Zr${\mathbb{R}}^4/{\mathbb{Z}}_r$. This circumvents case-by-case conjectures to be made in a wealth of examples found so far. In the 2d side, we successfully generate the super-Virasoro algebra and the proper screening charge in the q→−1$q\to -1$, t→−1$t\to -1$ limit, from the defining relation of the q-Virasoro algebra and the q  -deformed Heisenberg algebra. The central charge obtained coincides with that of the minimal series carrying odd integers of the N=1$N=1$ superconformal algebra. In the r-th root of unity limit in q in the 2d side, we give some evidence of the appearance of the parafermion-like currents. Exploiting the q-analysis literatures, q  -deformed su(n)$\mathit{su}(n)$ block is readily generated both at generic q,t$q,t$ and the r  -th root of unity limit. In the 4d side, we derive the proper normalization function for general (n,r)$(n,r)$ that accomplishes the automatic projection through the limit.     

Performance gain of displacement receiver with optimized prior probability

We numerically study the performance of the displacement based quantum receiver for the discrimination of weak 3- and 4-phase-shift keyed (PSK) coherent state signals. We show that due to the nontrivial asymmetry of the receiver structure, optimization of the prior probability increases the mutual information and achieves sub-shot-noise limit discrimination. Moreover, we estimate the cutoff rate for a 4-PSK signal and confirm that the prior probability optimization shortens the code length for a given decoding error criterion. Such consideration for the asymmetric channel matrix is essential in a study of the compassable quantum receiver.     

A new periodic pattern with five‐neighbored domain packing from ABC triblock terpolymer/B homopolymer blend

Self‐assembled structures from poly(isoprene‐b‐styrene‐b‐2‐vinylpyridine)(ISP)/styrene homopolymer blend were investigated. Five terpolymers whose total molecular weight, M, is in the narrow range of 121k < M < 214k, and volume fractions of the center block polystyrenes, ?_S, are similar at around 0.55, were prepared as parent block terpolymers. Their ?_P/?_I ratios, used as an indicator of asymmetry, are varied in the range 0.32 < ?_P/?_I < 2.46. Three low‐molecular weight styrene homopolymers with molecular weights of 3k, 9k, and 12k, respectively, were mixed with those block terpolymers to produce blends with almost constant styrene content within the range 0.65 < ?_S < 0.68. Both ISP/S(3k) and ISP/S(12k) blend series show a morphological transition from tetragonally packed cylinders (TPC) to double hexagonal structure (DHS) with hexagonally arrayed polyisoprene cylinders, each surrounded by six thin cylinders as satellites. If one focuses on ISP‐III(150k)/S blends whose ?_P/?_I is 0.88, TPC for ISP‐III/S(3k) was transformed to DHS for ISP‐III/S(12k), evidently due to the molecular weight effect of the added homopolymer. Finally a new periodic pattern, having P cylinders surrounded by five I cylinders each, has been discovered from ISP‐III/S(9k) at overall composition of ?_I/?_S/?_P = 0.17/0.68/0.15 and polystyrene block/styrene homopolymer ratio of w_S(b)/w_S(h) = 1.4. This structure was confirmed to possess hexagonal symmetry with larger unit cell than regular patterns ever known by X‐ray diffraction experiment. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 907–911     

Less than 10 defects/cm·μm in molecular beam epitaxy grown GaAs by arsenic cracking

Drastic reduction of irregular defect density in molecular beam epitaxy (MBE) grown GaAs is obtained by using a novel arsenic Knudsen effusion cell with a cracking furnace. A surface defect density of less than 10 cm⁻² is routinely achieved for continuously grown three 3-inch diameter, 1.7 μm thick, metal-semiconductor-field effect transistor (MESFET) structures when the cracking is carried out at about 700°C, which is the critical temperature for the conduction type change, and with the group III Knudsen cell only heated near the orifice of the crucible (top heat cell). These optimized cracking conditions also lead to successful mass production of some microwave devices with not only ultra-low defect density but suitable electrical performances.     

A new method of using supercritical carbon dioxide as a green solvent for synthesis and purification of 5,5‴-bis(tridecafluorohexyl)-2,2′:5′,2″:5″,2‴-quaterthiophene,which is one of n-type organic semiconducting materials

We have investigated synthesis as well as purification of 5,5?-bis(tridecafluorohexyl)-2,2′:5′,2″:5″,2?-quaterthiophene (BFH-4?T, n-type organic semiconducting material) using supercritical carbon dioxide (scCO₂) as a green solvent. BFH-4T was obtained in good selectivity and high yield by TDAE/PdCl₂-catalyzed reductive coupling reaction of 5-bromo-5′-(tridecafluorohexyl)-2,2′-bithiophene in scCO₂. We have also successfully established purification of the reaction mixture by passing scCO₂ in the reaction vessel. The product was yellow powder of BFH-4T with purity of more than 99% and Pd catalyst was not contained.     

5,12‐Diacetyl‐5,12‐dihydroquinoxalino[2,3‐b]quinoxalines: Solid‐State Fluorescence,AIE Properties,and Orbital Switching by Substituent Effect

The compound 5,12‐diacetyl‐5,12‐dihydroquinoxalino[2,3‐b]quinoxaline 1 a and its derivatives were prepared, and their solid‐ and solution‐state spectroscopic properties were studied; 1 a shows stronger fluorescence in solution than in the solid state due to aggregation caused by self‐quenching. Phenyl‐ or alkoxy‐substituted derivatives 1 b – d show solid‐state fluorescence with moderate quantum yields of about Φ=0.12–0.15, although the corresponding values are 0.01–0.07 in solution. The spectroscopic properties of alkoxy‐substituted derivatives were hardly changed compared to 1 a and 1 b , although 1 a and 1 b have similar absorption and fluorescence maxima in solution and in the solid state. DFT calculations indicate that orbital switching occurs between HOMO and HOMO‐1 and HOMO‐2 due to orbital interactions with introduced substituents. Crystal structure analysis revealed that the molecules have bent structures around tertiary nitrogen atoms and form a characteristic dimeric structure.