Sublattices of regular elements

Let L be an r-lattice, i.e., a modular multiplicative lattice that is compactly generated, principally generated, and has greatest element 1 compact. We consider certain subsets of L consisting of regular elements: there is a compact element with there is a principal element is a principal element with (0:X_{\alpha })=0\} . The first three subsets L_{f}, L_{sr}, and L_{r} are augmented filters on L, i.e., is a multiplicatively closed subset of $L$ with $A\in and $B\geq A$ with $B\in L$ implies $B\in and hence are sublattices of $L$ closed under multiplication. We first consider the more general situation of augmented filters on $L.$ These results are then applied to study the four previously defined subsets for $L$ an $r$-lattice or Noether lattice (i.e., an $r$-lattice with ACC). Finally, we give a brief discussion of how the results for augmented lattices can be applied to subsets of $L$ which are regular with respect to an $L$-module.     

Unbounded domains of normality

Let be a transcendental entire function of order less than 1/2. We introduce the method of ``self-sustaining spread' to study the components of the set of normality of such a function. We give a new proof of the fact that any preperiodic or periodic component of the set of normality of is bounded. We obtain the same conclusion for a wandering domain if the growth rate of is never too small.

     

The structure and transport properties of poly(methacrylic acid) in aqueous solution

Diffusion and anisotropic electrical conductivity measurements have been used to investigate the structure of poly(methacrylic acid) in aqueous solution at various degrees of neutralization. Both kinds of measurement indicate that the polyion chain opens from a coiled to an extended configuration as the chain is neutralized. In addition it was found that, at low concentrations, the opening of the chain is a two-step process, whereas at higher concentrations the mechanism involves a single step.     

Using direct electrochemistry to probe rate limiting events during nitrate reductase turnover

Protein film voltammetry of NarGH catalysing nitrate reduction under steady state conditions provides information on events occurring within the enzyme during the catalytic cycle. In this discussion we have focused on exploring the ability of two simple catalytic schemes to reproduce the voltammetric response of NarGH; electron transfer to the enzyme's active site being described either by interfacial electron exchange (Scheme 1) or intramolecular electron delivery via the operation of an electron relay centre (Scheme 2). When the two electron reduced, catalytically competent active site of the enzyme is generated from the oxidised form in 'rapid', non-rate limiting steps of the catalytic cycle, the voltammetric behaviour of NarGH cannot be reproduced. Rather under all the conditions investigated, one electron reduction of the active site from a semi-reduced to a fully-reduced state is found to be crucial to progression through the enzyme's catalytic cycle. The catalytically relevant semi- and fully-reduced oxidation states of the NarGH active site are most likely to correspond to the Mo(V) and Mo(IV) states of the Mo(MGD)2 centre, respectively, although it is not possible to rule out the possibility that they correspond to molybdopterin based oxidation states as observed in other enzymes. We suggest that the rate of either conformational rearrangement within the semi-reduced active site or intramolecular electron delivery to the active site constitutes a defining feature in the catalytic cycle of NarGH and results in the napp approximately 1 appearance of the catalytic waveform.     

Ceramic glaze analysis by simultaneous in-beam PGAA and XRFS

Twenty-one ready-to-use hobby glazes, of which 18 were labeled safe for food containers (SFFC), were analyzed for Al, B, Ba, Ca, Cd, Co, Cr, Cu, Fe, Gd, Hf, K, Mn, Na, Pb, Si, Sm, Sr, Ti, Zn, and Zr by neutron capture prompt -ray activation analysis (PGAA). Simultaneously, Pb was also determined by X-ray fluorescence spectrometry (XRFS) using Pb K X-rays induced by the -ray component of the neutron beam. The XRFS limits of detection were 200–400 g Pb·g^–1 (dry weight), a factor of 100 better than those for PGAA. Pb concentrations (by dry weight; with weight losses ranging from 28 to 49% after air-drying) found were 0.16–27.2% in the SFFC glazes and 0.86–32% in the other glazes. The SFFC glazes contained from <0.6 to 202 g Cd·g^–1, and Co, Cr, and Cu (elements which may enhance Pb leaching from fired glazes) were found in concentrations up to 1.2, 2.7, and 5.6%, respectively. Method accuracy was demonstrated with the analysis of soil, fly ash, and glass standard reference materials.     

Kinetics of the reaction of OH with HCl

The rate constant of the reaction OH + HCl → H₂O + Cl was measured in a flow tube over the temperature range 224 to 460°K using resonance fluorescence detection of OH. An Arrhenius expression k₁ = (2.0 ± 0.1) × 10^?12 exp [?(620 ± 20 cal/mole)/RT] was obtained. Stratospheric and reaction kinetic implications are discussed briefly.     

Reduction of the titanium niobium oxides. II. TiNb24O62

Interpretation of the reduction path of TiNb₂₄O₆₂ is complicated by uncertainty about both the stoichiometric ranges of the possible block structures and the formation of TiNb solid solutions. Reduction forms the Me₁₂O₂₉ phase, probably from the outset, with an initial composition close to Ti₂Nb₁₀O₂₉, thereby rapidly depleting the Me₂₅O₆₂ phase of titanium. When log p_O2 (atm) has dropped to ?9.62, a phase approximately Ti_0.95Nb_11.05O₂₉ is in equilibrium with titanium-free Nb₂₅O₆₂ at its lower composition limit (NbO_2.471). Nb₂₅O₆₂ is then reduced to Nb₄₇O₁₁₆ without change in the Me₁₂O₂₉. At ?9.62>log p_O2 (atm) > ?10.0, niobium is transferred to the Me₁₂O₂₉ phase and Nb₄₇O₁₁₆ is consumed. A second univariant equilibrium is set up as Nb₄₇O₁₁₆ is reduced to Nb₂₂O₅₄. This is consumed in turn, to increase the niobium content of the Me₁₂O₂₉ until, at log p_O2 close to ?10.8, monophasic Ti_0.48Nb_11.52O₂₉ is formed. The (Ti,Nb)O₂ solid solution then appears and the final product is Ti_0.04Nb_0.96O₂, with the rutile superstructure cell reported for NbO₂.     

Asymmetric aza-[2,3]-Wittig sigmatropic rearrangements: chiral auxiliary control and formal asymmetric synthesis of (2S, 3R, 4R)-4-hydroxy-3-methylproline and (-)-kainic acid

A survey of 16 different chiral auxiliaries and a variety of strategies found that an (-)-8-phenylmenthol ester of a glycine derived migrating group can control the absolute stereochemistry of aza-[2,3]-Wittig sigmatropic rearrangements with diastereoselectivities of ca. 3 : 1 with respect to the auxiliary. In two specific examples, ca. 50% yields of enantiomerically pure products were obtained after chromatographic purification. These were synthetically manipulated with no erosion of stereochemistry into intermediates that completed formal asymmetric syntheses of (+)-HyMePro and (-)-kainic acid.