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.

     

Analysis method of the angiotensin-I converting enzyme inhibitory activity based on micellar electrokinetic chromatography.

A micellar electrokinetic chromatography (MEKC) method was developed for estimating the angiotensin-I converting enzyme (ACE) inhibitory activity by separating the hippuric acid liberated in the ACE reaction mixture in the presence of an inhibitor, captopril. The hippuric acid was successfully separated and detected by MEKC with a 25 mM sodium dodecyl sulfate solution in a 25 mM phosphate-50 mM borate buffer at pH 7.0; the total analysis took about 5 min. A good linear relationship was observed between the inhibitor and the peak area of hippuric acid release. No significant difference in the ACE inhibitory activity (IC50) of captopril (an antihypertensive medicine) or autolyzed-mushrooms (functional foods) was observed between the conventional method and the MEKC method. The MEKC method was found to be a useful technique for a rapid assay of the ACE inhibitory activity.     

Anomalies of ultrasonic velocity in high-Tc ceramics YBa2Cu3Oy and BiSrCaCu2Oy

Ultrasonic longitudinal velocity and adsorption have been measured in ceramic superconductors YBa₂Cu₃O_y with various porosity and also in BiSrCaCu₂O_y. A velocity drop of about 400 ppm was found at T_c only in the measurements on cooling. The magnitude of the velocity drop is anomalously large compared with the value expected from the thermodynamics. A hysteresis of velocity with respect to temperature was observed in all the samples studied. It is suggested that some structural change at pore size level is responsible for this phenomenon.     

Magnetism in electron-doped copper oxides

We report muon spin relaxation/rotation measurements on sintered powder samples of Nd_2−x Ce _x CuO_4−y and a large single crystal of Nd₂CuO_4−y . We find an electronic phase diagram which is quite similar to that of hole-doped superconductors such as La_2−x Sr _x CuO_4−y , although the doping of electrons into the system is less efficient in destroying the static moments on the copper spins. Static magnetic order in Nd₂CuO_4−y appears below about 250 K, and two spin reorientations are seen atT=75 K andT=35 K. Measurements of the magnetic field penetration depth have been unsuccessful due to the rare-earth paramagnetism of these materials.     

Effect of annealing on structure and permeability of poly [(l-trimethylsilyl)-l-propyne]

The permeability of annealed poly (l-(trimethylsilyl)-l-propyne) was studied from the viewpoint of structural information obtained from x-ray diffraction and density. The sample cast from benzene solution had low density (0.82 g/cm³) and high permeability, whereas the annealed sample had a higher density (0.88 g/cm³) and permeability lower by two orders of magnitude. The smaller-angle x-ray diffraction peak for each sample, which was likely to reflect the distance between intermolecular chains, increased in intensity and shifted toward higher angle, corresponding to the change of the density with annealing. The logarithmic oxygen permeability was proportional to the density, namely the free volume fraction correlated with the diffusion coefficient and controlled by annealing and swelling by alcohols.     

Group symmetry in tensor categories and duality for orbifolds

A duality for orbifolds is presented as an application of group extensions in tensor categories.     

Uptake and excretion of total inorganic arsenic by the freshwater alga Chlorella vulgaris

Arsenic-tolerant freshwater alga Chlorella vulgaris which had been collected from an arsenicpolluted environment were tested for uptake and excretion of inorganic arsenic. Approximately half the quantity of arsenic taken up by C. vulgaris was estimated to be adhered to the extraneous coat (10 wt %) of the cell. The remainder was bioaccumulated by the cell. Both adhered and accumulated arsenic concentrations increased with an increase in arsenic(V) concentration of the aqueous phase. Arsenic(V) accumulation was affected by the growth phse: arsenic was most actively accumulated when the cell was exposed to arsenic during the early exponential phase and then accumulation decreased with an increase in culture time exposed to arsenic. The alga grew well in the modified Detmer (MD) medium containing 1 mg As(III) dm^?3 and the growth curve was approximated by a ‘logistic equation’. Arsenic(III) was accumulated up to the second day of the culture time and arsenic(III) accumulation decreased with an increase in the culture time after that. Arsenic accumulation was also largely affected by various nutrients, especially by managanese, iron and phosphorus compounds. A modified MD medium with the three nutrients was proposed for the purpose of effective removal of arsenic from the aqueous phase. Using radioactive arsenate (Na₂H⁷⁴AsO₄), the arsenic accumulated was found to be readily excreted under conditions which were unfavourable for the multiplication of C. vulgaris.