Some homological properties of commutative semitrivial ring extensions

LetR be a commutative ring with 1 andM anR-module. If:M _R MR is anR-module homomorphism satisfying(mm)=(mm) and(mm)m=m(mm), the additive abelian groupRM becomes a commutative ring, if multiplication is defined by (r,m)(r,m)=(rr+(mm),rm+rm). This ring is called the semitrivial extension ofR byM and and it is denoted byR M. This generalizes the notion of a trivial extension and leads to a more interesting variety of examples. The purpose of this paper is to studyR M; in particular, we are interested in some homological properties ofR M as that of being Cohen-Macaulay, Gorenstein or regular. A sample result: Let (R,m) be a local Noetherian ring,M a finitely generatedR-module and Im() m. ThenR M is Gorenstein if and only if eitherRM is Gorenstein orR is Gorenstein,M is a maximal Cohen-Macaulay module andMM ^*, where the isomorphism is given by the adjoint of.     

Speciation in the aqueous H+/H2VO4-/H2O2/picolinate system relevant to diabetes research

A detailed study of the quaternary aqueous H+/H2VO4-/H2O2/picolinate (Pi-) system has been performed at 25 degrees C in 0.150 M Na(Cl) medium using quantitative 51 V NMR (500 MHz) and potentiometric data (glass electrode). In the ternary H+/H2VO4-/Pi- system, six complexes have been found in the pH region 1-10. In the quaternary H+/H2VO4-/H2O2/Pi- system, eight additional complexes have been found. Generally, equilibria are fast in both systems. The rate of peroxide decomposition depends on the species in solution. Chemical shifts, compositions and formation constants for the species are given. Equilibrium conditions and the fit of the model to the experimental data are illustrated in distribution diagrams. Possible formation of mixed ligand species with imidazole, lactic acid and citric acid have been investigated and ruled out under the same experimental conditions. Structural proposals are given, based on 1)C NMR data and available crystal structures.     

Multicomponent polyanions. 57. Large-angle X-ray scattering study of aqueous molybdophenylphosphonate solutions

The radial distribution functions are calculated from large-angle X-ray scattering (LAXS) measurements for one concentrated aqueous molybdate/heptamolybdate solution and five aqueous molybdophenylphosphonate solutions (lithium chloride medium). Besides water and hydrated lithium, chloride, and molybdate ions, five species in all, having different nuclearities, are postulated to exist in the solutions, according to equilibrium studies using potentiometry and 31P NMR spectroscopy. The structures of the three polymolybdate species Mo7O24(6-), Mo8O26(4-), and (C6H5P)2Mo5O21(4-), for which the structures are determined crystallographically, are confirmed to exist also in aqueous solution. The principal structures of the remaining two complexes, (C6H5P)Mo6O21(OH2)5(2-) and (C6H5P)Mo7O25(OH2)4-, are elucidated with the use of structures of related species. Both anions have one group of four edge-sharing MoO6 octahedra and another group of two MoO6 octahedra connected by sharing corners, forming a bent unsymmetric six-membered ring, with the C6H5PO3 group placed on the crowded side of the ring. In the former, the group of two MoO6 octahedra is edge-shared, while in the latter, the group is face-shared, resulting in a ring small enough to tetrahedrally coordinate to the seventh molybdenum opposite the phenyl group.     

Dielectric relaxation studies of 1-hexanol and 1,2-hexanediol in heptane

Solutions of 1-hexanol and 1,2-hexanediol in heptane have been investigated tigated by means of dielectric time domain spectroscopy (TDS). The permittivity spectrum of 1-hexanol in heptane is characterized by a model function containing a sum of three elementary Debye dispersions, while 1,2-hexanediol in heptane is best described by a Cole-Davidson model function. It is shown that dilute solutions of 1-hexanol in heptane have a completely different behavior to that of 1,2-hexanediol. For the diol, the relaxation time levels off at a high value indicating an existence of higher hydrogen bonded complexes. It is possible to quantify the relative amount of monomeric 1-alcohol molecules from the dielectric spectrum. The monomerization rate for 1-hexanol upon dilution with heptane is initially low, but increases rapidly for mole fractions of heptane exceeding 0.4.     

A microwave-assisted click chemistry synthesis of 1,4-disubstituted 1,2,3-triazoles via a copper(I)-catalyzed three-component reaction

A microwave-assisted three-component reaction was used to prepare a series of 1,4-disubstituted-1,2,3-triazoles from corresponding alkyl halides, sodium azide, and alkynes. This procedure eliminates the need to handle organic azides, as they are generated in situ, making this already powerful click process even more user-friendly and safe.     

The rate of reduction of selenium(VI) to selenium(IV) in hydrochloric acid

The reduction of selenium(VI) to selenium(IV) in 4, 5 and 6M hydrochloric acid was studied at temperatures between 50 and 95 degrees . The reaction rate was determined by measurement of the selenium(IV) formed, by continuous-flow hydride-generation atomic-absorption spectrometry. The most notable feature of the reaction is the strong increase in rate with increasing hydrogen-ion concentration and temperature. The rate increases initially with chloride concentration at constant acidity (mixtures of hydrochloric and perchloric acid) but levels off to an almost constant value at high chloride concentrations.     

Dissociative recombination of the weakly bound NO-dimer cation: cross sections and three-body dynamics

Dissociative recombination (DR) of the dimer ion (NO)(2) (+) has been studied at the heavy-ion storage ring CRYRING at the Manne Siegbahn Laboratory, Stockholm. The experiments were aimed at determining details on the strongly enhanced thermal rate coefficient for the dimer, interpreting the dissociation dynamics of the dimer ion, and studying the degree of similarity to the behavior in the monomer. The DR rate reveals that the very large efficiency of the dimer rate with respect to the monomer is limited to electron energies below 0.2 eV. The fragmentation products reveal that the breakup into the three-body channel NO+O+N dominates with a probability of 0.69+/-0.02. The second most important channel yields NO+NO fragments with a probability of 0.23+/-0.03. Furthermore, the dominant three-body breakup yields electronic and vibrational ground-state products, NO(upsilon=0)+N((4)S)+O((3)P), in about 45% of the cases. The internal product-state distribution of the NO fragment shows a similarity with the product-state distribution as predicted by the Franck-Condon overlap between a NO moiety of the dimer ion and a free NO. The dissociation dynamics seem to be independent of the NO internal energy. Finally, the dissociation dynamics reveal a correlation between the kinetic energy of the NO fragment and the degree of conservation of linear momentum between the O and N product atoms. The observations support a mechanism in which the recoil takes place along one of the NO bonds in the dimer.     

Multiple binding modes of the camptothecin family to DNA oligomers

The binding constants of camptothecin, topotecan and its lactone ring-opened carboxylate derivative to DNA octamers were measured by UV and NMR spectroscopy. The self-association of topotecan (TPT) was also measured. The carboxylate form of TPT binds in the same way as the lactone, but more weakly. Titration of TPT into d(GCGATCGC)2 shows a preferred location stacked onto the terminal G1 base. However, the intermolecular NOEs cannot be reconciled with a single conformation of the complex, and suggest a model of a limited number of conformations in fast exchange. MD calculations on four pairs of starting structures with TPT stacked onto the G1-C8 base pair in different orientations were therefore performed. The use of selected experimental "docking" restraints yielded ten MD trajectories covering a wide conformational space. From a combination of calculated free energies, NOEs and chemical shifts, some of the structures produced could be eliminated, and it is concluded that the data are consistent with two major families of conformations in fast exchange. One of these is the conformation found in a crystal of a TPT/DNA/topoisomerase I ternary complex [Proc. Natl. Acad. Sci. USA 2002, 99, 15 387-15 392].     

pH sensitivity of Si--C linked organic monolayers on crystalline silicon surfaces.

The electrochemical behavior of Si--C linked organic monolayers is studied in electrolyte-insulator-Si devices, under conditions normally encountered in potentiometric biosensors, to gain fundamental knowledge on the behavior of such Si electrodes under practical conditions. This is done via titration experiments, Mott-Schottky data analysis, and data fitting using a site-binding model. The results are compared with those of native SiO(2) layers and native SiO(2) layers modified with hexamethyldisilazane. All samples display pH sensitivity. The number of Si--OH groups on the alkylated samples is calculated to be less than 0.7 % of that of a pure SiO(2) insulator, which still causes a pH sensitivity of approximately 25 mV per pH unit in the pH range: 4-7. The alkylated samples hardly suffer from response changes during up- and down-going titrations, which indicates that very little oxide is additionally formed during the measurements. The pK(a) values of all samples with monolayers (4.0-4.4) are lower than that of native SiO(2) (6.0). The long-term drift (of approximately 1 mV h(-1)) is moderate. The results indicate that biosensors composed of alkylated Si substrates are feasible if a cross-sensitivity towards pH in the sensor signal is taken into account.