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.

     

Interfacial adsorption state of protonated lipophilic porphyrins in a liquid-liquid system by using reflection spectrometry.

Analysis by reflection spectrometry was performed to clarify the interfacial adsorption of protonated lipophilic tetraphenylporphyrin derivatives in a dodecane-aqueous sulfuric acid system, and to confirm the utility of partial reflection spectroscopy. Interfacial adsorption was not observed for porphyrins substituted at the 2,6 positions of meso-phenyl groups, suggesting that the substituents prevent porphyrins from forming aggregates by steric hindrance. Polymorphous J-aggregates of acid dications were produced by tetra-p-tolylporphyrin with a saturated interfacial molecular density of 1.0 x 10(-10) mol cm(-2), which could yield 48 degrees as a mean tilting angle of the pyrrole ring plane from the interface normal. Partial-reflection spectrometry can provide sensitive detection and molecular orientation analysis of interfacial adsorbates.     

Compact directed acyclic word graphs for a sliding window

Suffix trees are a well-known and widely-studied data structure highly useful for string matching. The suffix tree of a string w can be constructed in O(n) time and space, where n denotes the length of w. Larsson achieved an efficient algorithm to maintain suffix trees for a sliding window. It contributes to prediction by partial matching (PPM) style statistical data compression scheme. Compact directed acyclic word graphs (CDAWGs) are a more space-economical data structure for indexing strings. In this paper we propose a linear-time algorithm to maintain CDAWGs for a sliding window.     

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     

Ferroelectric phase transitions in Pb2xSn2(1-x)P2Se6 system

Heat capacities of the Pb_2xSn_2(1-x)P₂Se₆ crystals (x=0, 0.098, 0.251, 0.402 and 1.0) were measured using an adiabatic calorimeter at temperatures between 10 and 350 K. In the crystal of x=0, two heat capacity anomalies corresponding to the ferroelectric commensurate - intermediate incommensurate(C-IC) phase transition temperature T _i, and the incommensurate - paraelectric (IC-N) phase transition temperature T _c, were observed at 193.24±0.10 and 220.07±0.15 K, respectively. The phase transition temperatures decreased with an increase in Pb²⁺ concentration. The anomaly at Ti disappeared at x=0.251 in the mixed systems of the Pb_2xSn_2(1-x)P₂Se₆. In the crystal of Pb₂P₂Se₆ (x=1.0), no phase transition was observed. The normal heat capacities for the mixed crystals were determined by least squares fitting of the Debye and Einstein functions to the experimental data. The anomalous heat capacities gave the phase transition entropies of 8.5 and 1.5 J mol^-1 K^-1 for x=0. The large transition entropies are consistent with an order-disorder mechanism in the ferroelectric-paraelectric phase transitions in x=0. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Stochastic phase lockings in a relaxation oscillator forced by a periodic input with additive noise: A first-passage-time approach

Noise effects on phase lockings in a system consisting of a piecewise-linear van der Pol relaxation oscillator driven by a periodic input are studied. The problem of finding the period of the oscillator is reduced to the first-passage-time problem of the Ornstein-Uhlenbeck process with time-varying boundary. The probability density functions of the first-passage time are used to define the operator which governs a transition of an input phase density after one cycle of the oscillator. Phase lockings in a stochastic sense are investigated on the basis of the density evolution by the operator.