Gamma and sine functions for Lie groups and period integrals

We study gamma and sine functions attached to a finite dimensional linear representation of a Lie group including their multiple versions via zeta regularizations. These definitions allow us to understand several multiple gamma and sine functions known so far, such as Barnes' gamma functions, Shintani's sine functions, and their q-analogues, in a unified way. Further, we discuss period integrals for such gamma functions.     

QuantumR matrices related to the spin representations ofB n andD n

We present the explicit form of the trigonometricR matrices related to the spin representations of the simple Lie algebrasX _n=B _n,D _n. We conjecture that one dimensional configuration sums of the corresponding vertex models in the face formulation are the string functions ofX _n ⁽¹⁾ modules.     

1H NMR spectra of 1-alkyl-1,2,3,4-tetrahydro-2-oxo-3-azocine-carboxylic acid derivatives and their analogues

¹H NMR spectra of 1-alkyl-1,2,3,4-tetrahydro-2-oxo-3-azocinecarboxylates and -carbonitriles indicated that the geminal protons at the 1-α-position were located in noneqnivalent magnetic environments. The difference in the chemical shifts amounted to as much as 0.73 ppm in the case of methyl 1-ethyl-1,2,3,4-tetrahydro-2-oxo-3-azocinecarboxylate at 26°, and the free energy of activation for the coalescence was estimated to be larger than 23 $\text{kcal}\text{mol}$. The same type of nonequivalence and coalescence phenomena were also observed even with dimethyl protons at the 1-γ-position of 1-isobutyl-1,2,3,4-tetrahydro-2-oxo-3-azocinecarboxylate (ΔG^≠_c = 19 $\text{kcal}\text{mol}$). The situation was hardly affected by the reduction of the CC double bonds. The nonequivalence was not observed, however, if the substituent at the 3-position was absent. Therefore, these novel ¹H NMR spectra of 1-alkyl protons in the title compounds were concluded to be due to strong coupling between the restricted rotation around N(1)—C(α) bond and inversion of the 2-oxoazocine ring which required high energy of activation.     

Potassium-selective membrane electrodes based on macrocyclic metacyclophanes analogous to calixarenes.

The tetrabutyl ester derived from 9,16,25,32-tetrahydroxy[3.1.3.1]metacyclophane was an excellent ionophore for constructing a K+-selective membrane electrode. This ionophore exhibited a much higher selectivity toward K+ than the structurally similar potassium ionophore IV commercially available from Fluka. In particular, the interference from organic ammonium ions decreased remarkably. Potassium ionophore IV possessed oxygen atoms in the ring structure, while the present ionophore changed the oxygen atoms to carbon atoms. Thus, the removal of oxygen atoms in ring constituents of the metacyclophane acted to reduce the interaction with the NH3+ group of organic ammonium ions. The size of the cavity of the present ionophore was between those of calix[4]arene and calix[6]arene derivatives, which act as Na+ and Cs+ ionophores, respectively, demonstrating that the ability to recognize alkali metal cations was strongly cavity size-dependent. The present K+-selective electrode had less interference from Rb+ and Cs+ than an electrode constructed using valinomycin, but suffered greater interference from Na+.     

Phyllurine, leaf-opening substance of a nyctinastic plant, Phyllanthus urinaria L.

We have isolated phyllurine (1) as the leaf-opening substance of Phyllanthus urinaria L. that keeps the Phyllanthus leaves open. 1 was quite effective for the leaf-opening of Phyllanthus urinaria L. at 2.5 ×10⁻⁵ M, but not effective for other nyctinastic plants even at 1 × 10⁻⁴ M. The leaf-closing substance of this plant has already been identified as phyllanthurinolactone (2). Thus, the leaf-movement of Phyllanthus urinaria L. is proposed to be controlled by the interaction between 1 and 2, similar to the case of Lespedza cuneata G. Don.     

Ultraviolet lasing and field emission characteristics of ZnO nano-rods synthesized by nano-particle-assisted pulsed-laser ablation deposition

We describe the lasing and the field emission characteristics of ZnO nano-rod crystals synthesized by nano-particle-assisted pulsed-laser ablation deposition, where nano-particles formed in the gas phase by the condensation of the laser-ablated species are transported on to the substrate to form nanorods. The nano-rod crystals having a hexagonal shape with a pyramidal top were synthesized on a sapphire substrate by a single-step process. The nano-rod crystals act as an efficient ultraviolet emitter showing the stimulated emission under an optical excitation and also act as field emitters with a current density of 1 mA/cm² at an electric field strength of 16 V/μm. PACS 42.70.Hj; 85.45.Db; 81.05.Ea; 81.15.Fy     

Tributyltin cyanide: A facile cyanating agent of acyl chlorides

Tributyltin cyanide was prepared from tributyltin chloride and potassium cyanide, and was found to be an efficient cyanation agent for acyl chlorides to give acyl cyanides in excellent yields.