Abstract. The convex subsemilattices of a semilattice E form a lattice Co(E) in the natural way. The purpose of this paper is to study how the properties of this lattice relate to the semilattice itself.
For instance, lower semimodularity of the lattice is equivalent, along with various properties, to the semilattice being a
tree. When E has more than two elements the lattice does, however, fail many common lattice-theoretic tests. It turns out that it is
more fruitful to describe those semilattices E for which every ``atomically generated' filter of Co(E) satisfies certain lattice-theoretic properties. 相似文献
Dimethyl 2-acetoxy- and dimethyl 2-benzoyloxy-benzoylphosphonate undergo cyclisation and deoxygenation in the presence of excess trimethyl phosphite to give dimethyl (3-methyl-1-benzofuran-2-yl)phosphonate and dimethyl (3-phenyl-1-benzofuran-2-yl)phosphonate, respectively. The reaction pathway has been shown to involve phosphite attack on initially formed tricyclic dioxaphospholane intermediates with the subsequent loss of two molecules of trimethyl phosphate. In the absence of additional trimethyl phosphite the initially formed tricyclic dioxaphospholane intermediates lose one molecule of trimethyl phosphate and then undergo a novel rearrangement to give β-ketophosphonates. The mechanism for this reaction helps explain some previously reported epoxide rearrangements. In contrast, the initially formed anionic intermediate from the reaction of dimethyl 2-benzoyloxymethylbenzoylphosphonate with trimethyl phosphite undergoes decomposition to give a carbene intermediate which is trapped by the trimethyl phosphite to give an ylidic phosphonate. 相似文献
Surface catalytic processes produce, under certain conditions, small clusters of adsorbed atoms or groups, called islands which, after they have been formed, move as individual entities. Here we consider the catalytic reduction of NO with hydrogen on platinum. (i) Using video field ion microscopy, we observe the dynamic motion of small hydroxyl islands on the Pt(001) plane; despite changes in their morphology, the islands dimensions are confined to values corresponding to 10 to 30 Pt atoms suggesting cooperative effects to be in operation. (ii) We construct an automaton (or lattice Monte-Carlo) model on the basis of a set of elementary processes governing the microscopic dynamics. The agreement between the simulation results and the experimental observations suggests a possible mechanism for the formation and dynamics of hydroxyl islands. 相似文献
The electrocatalytic CO2 reduction reaction (CO2RR) can dynamise the carbon cycle by lowering anthropogenic CO2 emissions and sustainably producing valuable fuels and chemical feedstocks. Methanol is arguably the most desirable C1 product of CO2RR, although it typically forms in negligible amounts. In our search for efficient methanol‐producing CO2RR catalysts, we have engineered Ag‐Zn catalysts by pulse‐depositing Zn dendrites onto Ag foams (PD‐Zn/Ag foam). By themselves, Zn and Ag cannot effectively reduce CO2 to CH3OH, while their alloys produce CH3OH with Faradaic efficiencies of approximately 1 %. Interestingly, with nanostructuring PD‐Zn/Ag foam reduces CO2 to CH3OH with Faradaic efficiency and current density values reaching as high as 10.5 % and ?2.7 mA cm?2, respectively. Control experiments and DFT calculations pinpoint strained undercoordinated Zn atoms as the active sites for CO2RR to CH3OH in a reaction pathway mediated by adsorbed CO and formaldehyde. Surprisingly, the stability of the *CHO intermediate does not influence the activity. 相似文献
The development of catalysts for Mannich-type reactions that afford anti-products with excellent diastereo- and enantioselectivities under mild conditions and low catalyst loadings (1-5 mol %) is reported. Based on principles gained from the study of (S)-proline-catalyzed Mannich-type reactions that afford enantiomerically enriched syn-products, (3R,5R)-5-methyl-3-pyrrolidinecarboxylic acid (RR35) has been designed to catalyze the direct enantioselective anti-selective Mannich-type reactions. Computational studies of the above reaction using HF/6-31G* level of theory suggested that this design would be highly effective. The catalyst was subsequently synthesized and studied in organocatalytic Mannich-type reactions between unmodified aldehydes and N-PMP-protected alpha-imino esters. In accord with the design principles and in quantitative agreement with the theoretical predictions, reactions catalyzed by this catalyst afforded anti-products in good yields with excellent diastereo- and enantioselectivities (anti:syn 94:6 to 98:2, >97 to >99% ee). 相似文献
Magnetic nanoparticles (MNPs) which exhibit magnetic and catalytic bifunctionalities have been widely accepted as one of the most promising nanoagents used in water purification processes. However, due to the magnetic dipole-dipole interaction, MNPs can easily lose their colloidal stability and tend to agglomerate. Thus, it is necessary to enhance their colloidal stability in order to maintain the desired high specific surface area. Meanwhile, in order to successfully utilize MNPs for environmental engineering applications, an effective magnetic separation technology has to be developed. This step is to ensure the MNPs that have been used for pollutant removal can be fully reharvested back. Unfortunately, it was recently highlighted that there exists a conflicting role between colloidal stability and magnetic separability of the MNPs, whereby the more colloidally stable the particle is, the harder for it to be magnetically separated. In other words, attaining a win-win scenario in which the MNPs possess both good colloidal stability and fast magnetic separation rate becomes challenging. Such phenomenon has to be thoroughly understood as the colloidal stability and the magnetic separability of MNPs play a pivotal role on affecting their effective implementation in water purification processes. Accordingly, it is the aim of this paper to provide reviews on (i) the colloidal stability and (ii) the magnetic separation of MNPs, as well as to provide insights on (iii) their conflicting relationship based on recent research findings.