When does the subadditivity theorem for multiplier ideals hold?

Demailly, Ein and Lazarsfeld proved the subadditivity theorem for multiplier ideals on nonsingular varieties, which states the multiplier ideal of the product of ideals is contained in the product of the individual multiplier ideals. We prove that, in the two-dimensional case, the subadditivity theorem holds on log terminal singularities. However, in the higher dimensional case, we have several counterexamples. We consider the subadditivity theorem for monomial ideals on toric rings and construct a counterexample on a three-dimensional toric ring.

     

Preparation of benzoylchitosans and their chiroptical properties in dilute solutions

Two benzoyl substituted chitosan derivatives, 3,6‐O‐dibenzoylchitosan (DBC) and 2‐N‐3,6‐O‐tribenzoylchitosan (TBC), were prepared, and their optical activities in organic solvent were investigated by circular dichroism (CD). For TBC, two splitting bands (a negative one at 288 nm and a positive one at 274 nm) corresponding to the ¹L_b transition of the benzoyl group were observed in chloroform and dichloromethane, while only a negative CD band was recorded in N, N‐dimethylformamide (DMF). These results indicated that the transition moments of benzoyl groups were orderly arranged along the helical polymer chain when TBC was dissolved in a solvent with low polarity, but the same ordered structure did not appear in a polar solvent of DMF. For DBC, only negative CD signals corresponding to the ¹L_b transition of the benzoyl group were observed, regardless of the solvent property, which indicated that the chromophores were not arranged in an ordered fashion with appropriate geometry to interact with one another to induce bi‐signate CD signals. Adding methanol or DMF to the solution of TBC/chloroform resulted in a progressive decrease of the intensity of the positive split band at 274 nm. The intensity of the positive band was weakened upon heating a solution of TBC/chloroform from 20 to 60 °C. The results suggested that the ordered arrangement of the chromophores in the TBC system was dependent on solvent and sensitive to temperature. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4107–4115, 2004     

Ultrahigh‐molecular‐weight‐polyethylene‐fiber surface treatment by electron‐beam‐irradiation‐induced graft polymerization and its effect on adhesion in a styrene–butadiene rubber matrix

Aiming to develop a high‐performance fiber‐reinforced rubber from styrene–butadiene rubber (SBR), we applied a special technique using electron‐beam (EB)‐irradiation‐induced graft polymerization to ultrahigh‐molecular‐weight‐polyethylene (UHMWPE) fibers. The molecular interaction between the grafted UHMWPE fibers and an SBR matrix was studied through the evaluation of the adhesive behavior of the fibers in the SBR matrix. Although UHMWPE was chemically inert, two monomers, styrene and N‐vinyl formamide (NVF), were examined for graft polymerization onto the UHMWPE fiber surface. Styrene was not effective, but NVF was graft‐polymerized onto the UHMWPE fibers with this special method. A methanol/water mixture and dioxane were used as solvents for NVF, and the effects of the solvents on the grafting percentage of NVF were also examined. The methanol/water mixture was more effective. A grafting percentage of 16.4% was the highest obtained. This improved the adhesive force threefold with respect to that of untreated UHMWPE fibers. These results demonstrated that EB irradiation enabled graft polymerization to occur even on the inert surface of UHMWPE fibers. However, the mechanical properties of the fibers could be compromised according to the dose of EB irradiation. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2595–2603, 2004     

Quasi-monocyclic near-infrared pulses with a stabilized carrier-envelope phase characterized by noncollinear cross-correlation frequency-resolved optical gating.

Precise characterization of noncollinear optical parametric amplifier idler pulses that have bandwidths of more than an octave with a center wavelength at 990 nm was demonstrated. The method employed was cross-correlation frequency-resolved optical gating with broadband sum-frequency mixing to take advantage of the idler's angular dispersion. Compression to near the transform limit was achieved to produce quasi-monocyclic near-infrared pulses by use of a deformable membrane mirror.     

Chemically modified proton‐conducting membranes based on sulfonated polyimides: Improved water stability and fuel‐cell performance

A series of branched/crosslinked sulfonated polyimide (B/C‐SPI) membranes were prepared and evaluated as proton‐conducting ionomers based on the new concept of in situ crosslinking from sulfonated polyimide (SPI) oligomers and triamine monomers. Chemical branching and crosslinking in SPI oligomers with 1,3,5‐tris(4‐aminophenoxy)benzene as a crosslinker gave the polymer membranes very good water stability and mechanical properties under an accelerated aging treatment in water at 130 °C, despite their high ion‐exchange capacity (2.2–2.6 mequiv g^?1). The resulting polymer electrolytes displayed high proton conductivities of 0.2–0.3 S cm^?1 at 120 °C in water and reasonably high conductivities of 0.02–0.03 S cm^?1 at 50% relative humidity. In a single H₂/O₂ fuel‐cell system at 90 °C, they exhibited high fuel‐cell performances comparable to those of Nafion 112. The B/C‐SPI membranes also displayed good performances in a direct methanol fuel cell with methanol concentrations as high as 50 wt % that were superior to those of Nafion 112. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3751–3762, 2006     

Simultaneous determination of hypoxanthine,inosine, inosine-5′-phosphate and adenosine-5′-phosphate with a multielectrode enzyme sensor

A multielectrode enzyme sensor for the simultaneous determination of adenosine-5′-phosphate (AMP), inosine-5′-phosphate (IMP), inosine (HXR) and hypoxanthine (HX)in fish meat was developed by assembling four enzyme sensors for AMP, IMP, HXR and HX in a flow cell. These compounds were determined from oxygen consumption according to the following reactions: AMP $\text{AD}$ IMP $\text{NT}$ HXR $\text{NP, PO}{}^{\mathrm{3?}}{}_4$ HX $\text{XO, O}{}_2$ Uric acid where AD is AMP deaminase, NT is 5′-nucleotidase, NP is nucleoside phosphorylase and XO is xanthine oxidase. Enzymes were covalently bound to a membrane prepared from cellulose triacetate, 1,8-diamino-4-aminomethyloctane and glutaraldehyde. Sensors for HX, HXR, IMP and AMP were prepared by attaching membranes of XO, XONP, XO NPNT, and of XONPNT and AD, respectively, to four oxygen electrodes. Samples extracted from sea bass, bream, flounder, abalone and arkshell were analyzed within 5 min, from the simultaneous response curves of the four electrodes. Results obtained by the multisensor system were in good agreement with those determined by each single electrode.     

Rearrangement reaction of N-halo-s-[(1,2-benzisoxazol-3-yl)methyl]-sulfoximine to the corresponding α-halo sulfoximine

The first example of the rearrangement reaction of N-halosulfoximine to α-halo sulfoximine is described.     

Emission of 2-phenylethanol from its β-d-glucopyranoside and the biogenesis of these compounds from [H8] l-phenylalanine in rose flowers

The hydrolysis of 2-phenylethyl β-d-glucopyranoside (3) was found to be partially inhibited by feeding with 2-phenyl-N-glucosyl-acetamidiumbromide (8), a β-glucosidase inhibitor, resulting in a decrease in the diurnal emission of 2-phenylethanol (2) from Rosa damascena Mill. flowers. Detection of [1,1,2,2′,3′,4′,5′,6′-²H₈]-2 and [1,2,2′,3′,4′,5′,6′-²H₇]-2 from R. ‘Hoh-Jun’ flowers fed with [1,1,2,2′,3′,4′,5′,6′-²H₈]-3 suggested that β-glucosidase, alcohol dehydrogenase, and reductase might be involved in scent emission. Comprehensive GC-SIM analyses revealed that [1,2,2,2′,3′,4′,5′,6′-²H₈]-2 and [1,2,2,2′,3′,4′,5′,6′-²H₈]-3 must be biosynthesized from [1,2,2,2′,3′,4′,5′6′-²H₈] l-phenylalanine ([²H₈]-1) with a retention of the deuterium atom at α-position of [²H₈]-1.