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.

     

Selective Propargylation of Carbonyl Compounds and Imines with Barium Reagents

A Barbier‐type regioselective propargylation of aldehydes and ketones with (3‐bromobut‐1‐ynyl)trimethylsilane has been achieved using reactive barium as a low‐valent metal in THF. Especially in the case of ketones, the corresponding homopropargylic alcohols form almost exclusively. In the reaction of α,β‐unsaturated carbonyl compounds, only 1,2‐adducts have been observed. This method is also applicable to propargylation of imines, and the corresponding homopropargylic amines are obtained regiospecifically in good yields with diastereomeric ratios of up to 87:13.     

Design and synthesis of labeling reagents (MS probes) for highly sensitive electrospray ionization mass spectrometry and their application to the detection of carbonyl, alcohol, carboxylic acid and primary amine samples.

Novel labeling reagents, called MS probes, which possess a positively charged quaternary amine moiety and can transform a neutral analyte into a charged compound by simply mixing with the analyte and allowing the mixture to stand from several minutes to 30 min at room temperature or while heating to 50 degrees C, were designed and synthesized for the highly sensitive detection of carbonyl, alcohol, carboxylic acid and primary amine samples by electrospray ionization mass spectrometry (ESI-MS). The positively charged products can be detected with high sensitivity in an ESI-MS system, which is the most popular liquid MS instrument. All of the labeled products showed a remarkably large increase in the molecular-ion peak abundance detection sensitivity of over 500-fold at picomolar concentration levels compared to that of unlabeled analytes in an ESI-MS system. These MS probes, used together with liquid MS detection, are widely applicable as a convenient method for the highly sensitive detection of less than picomolar levels of analytes, and therefore greatly enhance the power of ESI-MS analysis.     

Precise chelatometric titrations of zinc, cadmium, and lead with molecular spectroscopy.

Spectral data during a chelatometric titration were utilized for determining an equivalence point of the titration. Three-dimensional titration data were analyzed by fitting to a theoretical equation that was derived from equilibrium equations among a metal ion, an indicator and EDTA. The equation with optimized parameters successfully explained the three-dimensional titration data. This method was applied to EDTA titration systems of zinc, cadmium and lead with xylenol orange (XO) as an indicator. These systems were analyzed while taking the formation of 1:1 and 2:1 metal-indicator complexes into account. By this method, an accurate equivalence point was determined as well as stability constants and molar absorption spectra of metal-indicator complexes in each titration system. Moreover, the comparability among the concentrations of the metal standard solutions prepared from pure metals (Zn, Pb, and Cd) was also confirmed by the proposed evaluation method.     

Angular distribution of muon pairs produced by negative pions on deuterium and tungsten in terms of coherent states

Recently published data on thep _T dependence of the angular distributions of muon pairs produced in collisions of negative pions with deuterium and tungsten nuclei reveal an unexpected tendency. We show that the quantum statistical approach involving expansions in terms of coherent states leads in this case to an exact, non-perturbative result which in the lowest order approximation describes the observed trends with sufficient accuracy. In this procedure, the non-vanishing correlations between the coordinates and momenta of dimuons play a decisive role.     

FMS scheduling based on timed Petri Net model and reactive graph search

This paper presents a new scheduling method for manufacturing system based on the Timed Petri Net model and a reactive fast graph search algorithm. The following two typical problems are addressed in this paper. (1) Minimization of the maximum completion time. (2) Minimization of the total tardiness. As for the problem (1), a new search algorithm which combines the RTA^∗ and a rule-based supervisor is proposed. As for problem (2), the original Petri Net model is converted to its reverse model and the algorithm developed for the problem (1) is applied, regarding the due date as the starting time in the reverse model. Some numerical experiments are carried out to demonstrate usefulness of our algorithm.     

Numerical Study on Population Inversion and Lasing Conditions in an Optically Thick Recombining Helium Plasma

Lasing conditions for He I in a cold recombining helium plasma are numerically discussed including optical thicknesses. A collisional radiative model is used to calculate population densities. We discuss the effect of self absorptions by the background residual gas on the lasing conditions quantitatively. The optical thickness is essential in the calculation and affects the population inversions between level pairs of the singlet state drastically, while those of the triplet state are not affected very much. In the optically thin plasma, the laser lower levels of the singlet state depopulate mainly through radiative transitions. On the other hand, they depopulate mainly through electron collisional deexcitations in the optically thick plasma. Results of the calculations are verified by the spectroscopic observations of an arc-heated magnetically trapped expanding plasma jet generator which we developed. The requirement for the background pressure in which the lasing is possible is discussed quantitatively.     

Stability of the steady state for the Falk model system of shape memory alloys

In this article a stability result for the Falk model system is proven. The Falk model system describes the martensitic phase transitions in shape memory alloys. In our setting, the steady state is a nonlocal elliptic problem. We show the dynamical stability for the linearized stable critical point of the corresponding functional. Copyright © 2007 John Wiley & Sons, Ltd.