The topology determined by the symbolic powers of primary ideals

Let q be a p-primary ideal in a Noetherian ring R. The main theorem characterizes when the q-adic and q-symbolic topologies on R are linearly equivalent; that is, when there n kexists an integer k≥0 such that q⁽ⁿ⁾ ?q^n-k for all n≥k. Using this, it is shown that when this holds for q, then it holds for several other primary ideals related to q (both in R and in certain other rings related to R) and that the powers of q(ⁿ) are symbolic powers for all n≥k (so p has primary ideals all of whose powers are symbolic powers).     

Photoproduct channels from BrCD2CD2OH at 193 nm and the HDO + vinyl products from the CD2CD2OH radical intermediate

We present the results of our product branching studies of the OH + C(2)D(4) reaction, beginning at the CD(2)CD(2)OH radical intermediate of the reaction, which is generated by the photodissociation of the precursor molecule BrCD(2)CD(2)OH at 193 nm. Using a crossed laser-molecular beam scattering apparatus with tunable photoionization detection, and a velocity map imaging apparatus with VUV photoionization, we detect the products of the major primary photodissociation channel (Br and CD(2)CD(2)OH), and of the secondary dissociation of vibrationally excited CD(2)CD(2)OH radicals (OH, C(2)D(4)/CD(2)O, C(2)D(3), CD(2)H, and CD(2)CDOH). We also characterize two additional photodissociation channels, which generate HBr + CD(2)CD(2)O and DBr + CD(2)CDOH, and measure the branching ratio between the C-Br bond fission, HBr elimination, and DBr elimination primary photodissociation channels as 0.99:0.0064:0.0046. The velocity distribution of the signal at m/e = 30 upon 10.5 eV photoionization allows us to identify the signal from the vinyl (C(2)D(3)) product, assigned to a frustrated dissociation toward OH + ethene followed by D-atom abstraction. The relative amount of vinyl and Br atom signal shows the quantum yield of this HDO + C(2)D(3) product channel is reduced by a factor of 0.77 ± 0.33 from that measured for the undeuterated system. However, because the vibrational energy distribution of the deuterated radicals is lower than that of the undeuterated radicals, the observed reduction in the water + vinyl product quantum yield likely reflects the smaller fraction of radicals that dissociate in the deuterated system, not the effect of quantum tunneling. We compare these results to predictions from statistical transition state theory and prior classical trajectory calculations on the OH + ethene potential energy surface that evidenced a roaming channel to produce water + vinyl products and consider how the branching to the water + vinyl channel might be sensitive to the angular momentum of the β-hydroxyethyl radicals.     

Thermal decomposition of generation-4 polyamidoamine dendrimer films: decomposition catalyzed by dendrimer-encapsulated Pt particles

The thermal decomposition of hydroxyl-terminated generation-4 polyamidoamine dendrimer (G4OH) films deposited on Au surfaces has been compared with decomposition of the same dendrimer encapsulating an approximately 40-atom Pt particle (Pt-G4OH). Infrared absorption reflection spectroscopy studies showed that, when the films were heated in air to various temperatures up to 275 degrees C, the disappearance of the amide vibrational modes occurred at lower temperature for the Pt-G4OH film. Dendrimer decomposition was also investigated by thermogravimetric analysis (TGA) in both air and argon atmospheres. For the G4OH dendrimer, complete decomposition was achieved in air at 500 degrees C, while decomposition of the Pt-G4OH dendrimer was completed at 400 degrees C, leaving only platinum metal behind. In a nonoxidizing argon atmosphere, a greater fraction of the G4OH decomposed below 300 degrees C, but all of the dendrimer fragments were not removed until heating above 550 degrees C. In contrast, Pt-G4OH decomposition in argon was similar to that in air, except that decomposition occurred at temperatures approximately 15 degrees C higher. Thermal decomposition of the dendrimer films on Au surfaces was also studied by temperature programmed desorption (TPD) and X-ray photoelectron spectroscopy (XPS) under ultrahigh vacuum conditions. Heating the G4OH films to 250 degrees C during the TPD experiment induced the desorption of large dendrimer fragments at 55, 72, 84, 97, 127, 146, and 261 amu. For the Pt-G4OH films, mass fragments above 98 amu were not observed at any temperature, but much greater intensities for H(2) desorption were detected compared to that of the G4OH film. XPS studies of the G4OH films demonstrated that significant bond breaking in the dendrimer did not occur until temperatures above 250 degrees C and heating to 450 degrees C caused dissociation of C=O, C-O, and C-N bonds. For the Pt-G4OH dendrimer films, carbon-oxygen and carbon-nitrogen bond scission was observed at room temperature, and further decomposition to atomic species occurred after heating to 450 degrees C. All of these results are consistent with the fact that the Pt particles inside the G4OH dendrimer catalyze thermal decomposition, allowing dendrimer decomposition to occur at lower temperatures. However, the Pt particles also catalyze bond scission within the dendrimer fragments so that decomposition of the dendrimer to gaseous hydrogen is the dominant reaction pathway compared to desorption of the larger dendrimer fragments observed in the absence of Pt particles.     

Sequencing inputs to multi-commodity pipelines

This paper examines the problem of sequencing the input of commodities, e.g. petroleum products, to a pipeline so that a surrogate for pumping and maintenance costs is minimized. This problem is complicated by the need to impose a discrete framework which handles the sequencing choices on a continuous flow problem. By focusing on the discrete aspects of the problem, the proposed model allows decomposition of the sequencing problem into subproblems which can be easily priced out in a branch-and-bound algorithm. Computational results on data generated to mimic a large U.S. petroleum pipeline are presented. These results show that the branch-and-bound algorithm only explores a small region of the solution space within a reasonable amount of time, less than 2.5 minutes to optimally sequence deliveries to twenty-four destinations.