Non-very ample configurations arising from contingency tables

In this paper, it is proved that, if a toric ideal possesses a fundamental binomial none of whose monomials is squarefree, then the corresponding semigroup ring is not very ample. Moreover, very ample semigroup rings of Lawrence type are discussed. As an application, we study very ampleness of configurations arising from contingency tables.     

Synthesis of (+)-goniopypyrone and (+)-goniotriol using Pd-catalyzed carbonylation

Syntheses of (+)-goniopypyrone and (+)-goniotriol isolated from Goniothalamus giganteus were achieved. The key steps involve Pd-catalyzed carbonylation for lactone ring formation and diastereoselective reduction of ynone using the (R)-CBS catalyst and borane dimethyl sulfide complex.     

Experimental Discussion on Eye-Safe 1.54 μm Photon Counting Lidar Using Avalanche Photodiode

A Mie hdar system with an eye-safe wavelength of 1.54 m was developed and its performance characteristics were experimentally discussed. The wavelength was generated by a Nd:YAG based methane-shifted Raman laser. The collected backscattering light was detected by an InGaAs avalanche photodiode working in photon counting mode at that wavelength. Results of atmospheric observation showed clearly the dynamics of multi-layered cluds up to an altitude of 7 km. The systems performance was confirmed on the point of signal to noise ratio in both the observation and the simulation. Advantages of the eye-safe 1.54 m wavelength in lidar atmospheric research and system limitations were discussed. © 2004 The Optical Society of Japan     

Quadratic initial ideals of root systems

Let be one of the root systems , , and and write for the set of positive roots of together with the origin of . Let denote the Laurent polynomial ring over a field and write for the affine semigroup ring which is generated by those monomials with , where if . Let denote the polynomial ring over and write for the toric ideal of . Thus is the kernel of the surjective homomorphism defined by setting for all . In their combinatorial study of hypergeometric functions associated with root systems, Gelfand, Graev and Postnikov discovered a quadratic initial ideal of the toric ideal of . The purpose of the present paper is to show the existence of a reverse lexicographic (squarefree) quadratic initial ideal of the toric ideal of each of , and . It then follows that the convex polytope of the convex hull of each of , and possesses a regular unimodular triangulation arising from a flag complex, and that each of the affine semigroup rings , and is Koszul.     

Synthesis and photochromism of spirobenzopyrans and spirobenzothiapyran derivatives bearing monoazathiacrown ethers and noncyclic analogues in the presence of metal ions

Spirobenzopyrans bearing monoazathiacrown ethers and noncyclic analogues were synthesized, and their ion-responsive photochromism depending on the dual metal ion interaction with the crown ether and the phenolate anion moieties was examined using alkali and alkaline-earth metal ions, Ag(+), Tl(+), Pb(2+), Hg(2+), and Zn(2+). The prepared spirobenzopyrans showed a selective binding ability to Mg(2+) and Ag(+) with negative and positive photochromism, respectively. Among the metal ions, only Ag(+) facilitated photoisomerization to the corresponding merocyanine form. Depending on the ring size of the monoazathiacrown ether moieties, soft metal ions such as Hg(2+) and Ag(+) showed significant shifts in the UV-vis absorption spectra, while hard metal ions such as Mg(2+), Zn(2+), and Pb(2+) did not afford any meaningful shift. This result reflects that the monoazathiacrown ether and phenolate anion moieties prefer soft and hard metal ions, respectively. Therefore, the Mg(2+) and Ag(+) selectivities are mainly derived from the phenolate anion and monoazathiacrown ether moieties, respectively. On the other hand, a spirobenzothiapyran bearing 3,9-dithia-6-monoazaundecane showed a remarkable selectivity to Ag(+).     

Polymerization of coordinated monomers. XIV. Systematic deviations from alternating regulation in copolymerization of methyl methacrylate with styrene in the presence of metal halides

Methyl methacrylate (MMA) and styrene (St) copolymerize in the presence of zinc chloride at 3°C under photoirradiation. The contents of methyl methacrylate in the copolymers obtained at a [ZnCl₂]/[MMA] molar ratio of 0.4 are systematically larger than 53 mole %, which is the limiting value at a small feed ratio of methyl methacrylate. The resulting copolymers are confirmed as the sole products and not the mixtures by thin layer chromatography. The effect of dilution of the monomer feed mixture with toluene on copolymer composition suggests that it depends chiefly on the feed concentration of styrene and hardly at all on monomer feed ratios. Copolymerizations are also conducted in the presence of stannic chloride at ?17°C under photoirradiation and in the presence of ethylaluminium sesquichloride at 0°C with spontaneous initiation. The contents of methyl methacrylate in both copolymers obtained at feed ratios lower than 60 mole % almost correspond to the 1:1 alternating copolymer and increase systematically with higher feed ratios. The systematic deviations of copolymer composition obtained in the presence of metal halides are reasonably interpreted by the participation of the binary molecular complex composed of metal halide and methyl methacrylate in the polymerization of the ternary molecular complex composed of metal halide, methyl methacrylate, and styrene.     

Copper L X-ray spectra measured by a high resolution ion-induced X-ray spectrometer

High resolution L X-ray emission spectra of Cu have been measured by 0.75 MeV/u H, He, and F, 0.73 MeV/u Ar, 0.64 MeV/u Si, and 0.073 MeV/u Si ion impacts with a crystal spectrometer. The X-ray transition energies in the Cu target for Lι, Lη, L_1,2, Lβ₁, and Lβ_3,4 diagram lines induced by H ion impact are determined, which are in good agreement with those given in the reference by Bearden (Rev. Mod. Phys. 39, 78, 1967). The X-ray spectra produced by F, Si, and Ar ions have complicated structures due to multiple L and M shell vacancy production. The L_1,2 and Lβ₁ emission spectra for H and He ions are compared with the calculated ones based on the multiconfiguration Dirac-Fock method. The origin of the broadening of the L_1,2 line to the lower energy for H ion impact is attributed to one 2p plus one 3d electron vacancy production.     

Second-order necessary and sufficient optimality conditions for minimizing a sup-type function

In this paper, we give second-order necessary and sufficient optimality conditions for a minimization problem of a sup-type functionS(x)=sup{f(x,t);t T}, whereT is a compact set in a metric space and f is a function defined on ⁿ ×T. Our conditions are stated in terms of the first and second derivatives of f(x, t) with respect tox, and involve an extra term besides the second derivative of the ordinary Lagrange function. The extra term is essential when {f(x,t)} _t forms an envelope. We study the relationship between our results, Wetterling [14], and Hettich and Jongen [6].     

Electron spin resonance study on homogeneous catalysts derived from n-butyl titanate and triethylaluminum

ESR spectra of homogeneous catalyst systems derived from n-butyl titanate and triethylaluminum at Al/Ti molar ratios of 1.0–10 were observed in toluene solution at several temperatures from ?78°C to +25°C. In the whole range of Al/Ti molar ratios, a single signal with a g value of 1.951 was observed at ?78°C and was associated with the first reaction intermediate. With increasing temperature, the intensity of the signal decreased gradually, while two series of signals appeared, depending on the Al/Ti molar ratio. At an Al/Ti molar ratio of 1.7, seven kinds of signals with g values of 1.960, 1.946, 1.950, 1.959, 1.980, 1.977, and 1.978, respectively, were observed. On the other hand, four kinds of signals with g values of 1.934, 1.966, 1.952, and 1.979, respectively, were found at Al/Ti molar ratios larger than 3. The structures of the species corresponding to the signals were discussed on the basis of the ESR spectra, the order of their growth and their hyperfine structures being considered. Two series of ESR signal were correlated to two kinds of active species for polymerization of styrene and butadiene, respectively.