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.

     

Hydrometallation of 1-alkyl-3-trifluoromethyl propargyl alcohols

The hydrometallation of trifluoromethylated propargyl alcohol derivatives with metal hydride reagents proceeds smoothly to give cis- and trans-olefins on H₂O quenching. The halodemetallation of intermediate formed in the reaction process was also examined.     

Characterization of amperometry for in vivo measurement of dopamine dynamics in the rat brain

Constant potential amperometry with Nafion-coated carbon-fiber electrodes has been evaluated as a technique for in vivo detection of the neurotransmitter dopamine. The results of this technique have been compared to results obtained with fast-scan cyclic voltammetry at the same electrode during release of dopamine into the extracellular space of the brain during electrical stimulation of neurons. The data indicate that constant potential amperometry is a viable technique for detecting low concentrations of dopamine. Dopamine permeates the film more quickly with constant-potential amperometry than with repeated fast-scan cyclic voltammetry as predicted by diffusion equations. For the case of cyclic voltammetry, it is demonstrated that the temporal delay caused by diffusion through Nafion film can be removed by deconvolution procedures. Despite the suitability of constant potential amperometry as an in vivo monitoring technique, it does have several disadvantages when compared to fast-scan cyclic voltammetry. The diffusion layer extends outside of the Nafion film making determination of concentration based on in vitro calibrations more difficult to interpret. The reported concentrations are larger than obtained by cyclic voltammetry, a technique with the diffusion layer restricted to the Nafion film, and this result is likely an underestimation of the effect of the catalytic reaction between the o-quinone of dopamine and ascorbate. Amperometry was found to provide only slightly improved signal-to-noise ratios than cyclic voltammetry despite the use of greater filtering. This was because the advantage of dopamine accumulation in the film was lost. In addition, the small magnitude of the amperometric signal makes it more susceptible to electrical interference.     

Design of Ratiometric Fluorescent Probes Based on Arene–Metal‐Ion Interactions and Their Application to CdII and Hydrogen Sulfide Imaging in Living Cells

Non‐coordinative interactions between a metal ion and the aromatic ring of a fluorophore can act as a versatile sensing mechanism for the detection of metal ions with a large emission change of fluorophores. We report the design of fluorescent probes based on arene–metal‐ion interactions and their biological applications. This study found that various probes having different fluorophores and metal binding units displayed significant emission redshift upon complexation with metal ions, such as Ag^I, Cd^II, Hg^II, and Pb^II. X‐ray crystallography of the complexes confirmed that the metal ions were held in close proximity to the fluorophore to form an arene–metal‐ion interaction. Electronic structure calculations based on TDDFT offered a theoretical basis for the sensing mechanism, thus showing that metal ions electrostatically modulate the energy levels of the molecular orbitals of the fluorophore. A fluorescent probe was successfully applied to the ratiometric detection of the uptake of Cd^II ions and hydrogen sulfide (H₂S) in living cells. These results highlight the utility of interactions between arene groups and metal ions in biological analyses.     

Solving the Huff-Based Competitive Location Model on a Network with Link-Based Demand

This paper shows a computational method for optimizing the location of a store on a network in a competitive environment, assuming that consumers probabilistically choose stores following the Huff model (1963) and that the store can be located on a continuum of a network. This method gives the exact optimal solution with the computational order of n _N ² logn _N where n _N is the number of nodes of the network.     

Good ideals in Gorenstein local rings

Let be an -primary ideal in a Gorenstein local ring (, ) with , and assume that contains a parameter ideal in as a reduction. We say that is a good ideal in if is a Gorenstein ring with . The associated graded ring of is a Gorenstein ring with if and only if . Hence good ideals in our sense are good ones next to the parameter ideals in . A basic theory of good ideals is developed in this paper. We have that is a good ideal in if and only if and . First a criterion for finite-dimensional Gorenstein graded algebras over fields to have nonempty sets of good ideals will be given. Second in the case where we will give a correspondence theorem between the set and the set of certain overrings of . A characterization of good ideals in the case where will be given in terms of the goodness in their powers. Thanks to Kato's Riemann-Roch theorem, we are able to classify the good ideals in two-dimensional Gorenstein rational local rings. As a conclusion we will show that the structure of the set of good ideals in heavily depends on . The set may be empty if , while is necessarily infinite if and contains a field. To analyze this phenomenon we shall explore monomial good ideals in the polynomial ring in three variables over a field . Examples are given to illustrate the theorems.

     

Skeins associated with Homfly and Kauffman polynomials and invariants of graphs

In this article, we treat skeins associated with Homfly and Kauffman polynomials. Several properties of skeins are studied, and as an application, we construct invariants of trivalent graphs in S³.     

Effects of three dithiocarbamates on tissue distribution and excretion of cadmium in mice

N-Benzyl-D-glucamine dithiocarbamate (BGD), N-p-hydroxymethylbenzyl-D-glucamine dithiocarbamate (HBGD), and N-p-carboxybenzyl-D-glucamine dithiocarbamate (CBGD) were compared for their relative efficacies in the distribution and excretion of cadmium in mice exposed to cadmium. Mice were injected intraperitoneally with 109CdCl2 (1 mg of Cd/kg and 2 microCi of 109Cd/one animal). Three days later, they were injected with chelating agents (400 mumol/kg) every other day for 2 weeks. After injections of BGD and HBGD, cadmium was excreted mainly in the feces through the bile, and the fecal excretion of cadmium by HBGD was significantly higher than that by BGD or CBGD. These chelating agents increased the urinary excretion of cadmium to a small extent. The hepatic cadmium content was decreased only after HBGD injection. Also, the injection of HBGD caused a much greater decrease in renal cadmium content than did BGD or CBGD. These chelating agents did not result in the redistribution of cadmium to the brain, testes, or heart. The growth of mice was only slightly retarded by injections of these chelating agents. The results of this study indicate that the injection of HBGD to mice pretreated with cadmium can remove cadmium from the body, mainly through fecal excretion, without redistribution of cadmium to other tissues such as the brain, testes, and heart, more effectively than BGD or CBGD.     

HPLC separation of all aldopentoses and aldohexoses on an anion-exchange stationary phase prepared from polystyrene-based copolymer and diamine: the effect of NaOH eluent concentration

To investigate the separations of all aldopentoses (ribose, arabinose, xylose and lyxose) and aldohexoses (glucose, galactose, allose, altrose, mannose, gulose, idose and talose) on the D? stationary phase prepared by the reaction of chloromethylated styrene-divinylbenzene copolymer and N,N,N',N'-tetramethyl-1,6-diaminohexane, we examined the effect of varying the concentration of the NaOH eluent on the elution orders. Separations of these aldoses were achieved using a 20 mM NaOH eluent. The elution behaviors of the aldoses were probably due to not only the individual pK(a) values, but also the chemical structures of the cyclic aldoses.