Local cohomology with support in a parameter ideal

Motivated in part by an attempt to understand better the notion of a parameter-like sequence introduced in Hochster (2003) [7, (2.2)], we study results concerning the heights of the annihilators and the finiteness of the dimension of the socle in certain local cohomology modules with support in a parameter ideal. We obtain positive results under certain hypotheses of low dimension or codimension, but we also find examples that show, in the general case, that support in a parameter ideal does not restrict the behavior of local cohomology much more than support in an arbitrary ideal. The results obtained here strongly suggest that it would be worthwhile to seek a modification of the notion of a parameter-like sequence introduced in [7].     

High critical currents for dendrite penetration and voiding in potassium metal anode solid-state batteries

Journal of Solid State Electrochemistry - Potassium metal anode solid-state cells with a K-beta”-alumina ceramic electrolyte are found to have relatively high critical currents for dendrite...     

Dynamics of swelling/contracting hard spheres surmised by an irreversible Langevin equation

The diffusion of molecules through uniform homogeneous materials can readily be described by Brownian motion or generalizations thereof. The further generalization of these models to describe molecular diffusion through heterogeneous and nonstationary solvents is much less understood. Phenomenological nonstationary generalizations of the generalized Langevin equation (GLE) have earlier been developed satisfying the fluctuation-dissipation relationship in quasi-equilibrium limits while exhibiting somewhat complex behavior away from equilibrium. This reduced-dimensional representation should be capable of describing the diffusion of a particle through a colloidal suspension whose average particle size is tuned by an external driving force such as pH. A simple particle model of such a process involves the motion of a hard-sphere particle in an explicit environment of swelling hard spheres. The velocity autocorrelation functions observed in a large number of simulations of the particle model under various swelling rates agree precisely with those of a single form of the nonstationary phenomenological model. Though this procedure is not an explicit projection of the mechanical system onto the nonstationary GLE, it does show that the latter correctly describes the dynamics of the projected coordinate--namely, diffusion of the solute--under nonequilibrium conditions. Both nonequilibrium solvent models lead to behavior reminiscent of beta-relaxation processes at packing fractions substantially below that of the glass transition.     

Study of overload for basic compounds in reversed-phase high performance liquid chromatography as a function of mobile phase pH

The retention and overloading properties for eight basic solutes and two quaternary ammonium compounds were studied over the pH range 2.7-10.0 using phosphate and carbonate buffers. At low pH, a hybrid inorganic-organic silica-ODS phase (XTerra RP-18, 15 cm x 0.46 cm) showed substantial loss in efficiency when sample masses exceeded about 0.5 microg; these results were similar to those obtained previously on pure silica ODS and wholly polymeric phases, suggesting a common overloading mechanism. At pH 7-8.5, substantial improvements in loading capacity were obtained on XTerra due apparently to the unexpectedly strong influence of small decreases in solute ionisation. Data from the quaternary compounds suggested that silanol ionisation on this phase was still small even at intermediate pH. For many bases, loading capacity continued to improve as the pH was raised to 10, in line with the decrease in the proportion of ionised solute. However, for the highest pK(a) solutes, peak shape worsened at high pH, possibly due to the negative influence of increasing column silanol ionisation.     

Electron-acceptor-induced isomerization of aryl [6,5] open fulleroids to [6,6] closed methanofullerenes and the electrochemical evaluation of their free energy difference

The thermal and photochemical rearrangements of a series of aryl substituted [6,5] open fulleroids to [6,6] closed methanofullerenes are accelerated in the presence in of electron acceptors. These [6,5] open fulleroids, facilitated by electron acceptors, rearrange thermally by a zwitteronic-type intermediate, while the photochemical reactions proceed via an excited-state electron-transfer process. The oxidation potentials of these [6,5] open fulleroids and their corresponding [6,6] closed methanofullerenes isomers have been evaluated. The free energy difference between the [6,5] open fulleroids and their corresponding [6,6] closed isomers have been estimated from the difference in their oxidation potentials.     

Functional relationships of multiparticle distribution functions obtained from the virial theorem

The He(I) photoelectron spectrum of the N₃(X ²H) radical, produced by the rapid gas phase reaction of fluorine atoms with hydrazoic acid, has been recorded. Three bands were observed corresponding to ionization of N₃(X 2H) to the N₃ ⁺ X ³Σ^?, ¹Δ and ¹Σ⁺ states. The vertical ionization energies to the observed ionic states were compared with those obtained from ΔSCF ab initio calculations. Evidence is presented to show that the major pathway of the F+HN₃ reaction occurs via a long-lived intermediate and involves abstraction of a hydrogen atom yielding vibrationally excited HF and the N₃ radical. Consideration of both the photoelectron data and a recent chemiluminescence study of the reaction has led to some re-interpretation of the latter results.     

Bis-functionalized fullerene-dibenzo[18]crown-6 conjugate: synthesis and cation-complexation dependent redox behavior

A one-step synthesis of bis-pyrrolidine functionalized fullerene-dibenzo[18]crown-6 conjugate and its metal cation complexation to the crown ether entity dependent redox behavior is reported.