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Susana Estopiñá-Durán Liam J. Donnelly Euan B. Mclean Bryony M. Hockin Prof. Alexandra M. Z. Slawin Dr. James E. Taylor 《Chemistry (Weinheim an der Bergstrasse, Germany)》2019,25(15):3950-3956
A combination of pentafluorophenylboronic acid and oxalic acid catalyses the dehydrative substitution of benzylic alcohols with a second alcohol to form new C−O bonds. This method has been applied to the intermolecular substitution of benzylic alcohols to form symmetrical ethers, intramolecular cyclisations of diols to form aryl-substituted tetrahydrofuran and tetrahydropyran derivatives, and intermolecular crossed-etherification reactions between two different alcohols. Mechanistic control experiments have identified a potential catalytic intermediate formed between the aryl boronic acid and oxalic acid. 相似文献
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This paper deals mainly with generalizations of results in finitary combinatorics to infinite ordinals. It is well-known that for finite ordinals ∑bT<αβ is the number of 2-element subsets of an α-element set. It is shown here that for any well-ordered set of arbitrary infinite order type α, ∑bT<αβ is the ordinal of the set M of 2-element subsets, where M is ordered in some natural way. The result is then extended to evaluating the ordinal of the set of all n-element subsets for each natural number n ≥ 2. Moreover, series ∑β<αf(β) are investigated and evaluated, where α is a limit ordinal and the function f belongs to a certain class of functions containing polynomials with natural number coefficients. The tools developed for this result can be extended to cover all infinite α, but the case of finite α appears to be quite problematic. 相似文献
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It is proved that the variety of relevant disjunction lattices has the finite embeddability property. It follows that Avron's relevance logic RMI min has a strong form of the finite model property, so it has a solvable deducibility problem. This strengthens Avron's result that RMI min is decidable. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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James K. Freericks Elliott H. Lieb Daniel Ueltschi 《Communications in Mathematical Physics》2002,227(2):243-279
The Falicov–Kimball model is a simple quantum lattice model that describes light and heavy electrons interacting with an
on-site repulsion; alternatively, it is a model of itinerant electrons and fixed nuclei. It can be seen as a simplification
of the Hubbard model; by neglecting the kinetic (hopping) energy of the spin up particles, one gets the Falicov–Kimball model.
We show that away from half-filling, i.e. if the sum of the densities of both kinds of particles differs from 1, the particles
segregate at zero temperature and for large enough repulsion. In the language of the Hubbard model, this means creating two
regions with a positive and a negative magnetization.
Our key mathematical results are lower and upper bounds for the sum of the lowest eigenvalues of the discrete Laplace operator
in an arbitrary domain, with Dirichlet boundary conditions. The lower bound consists of a bulk term, independent of the shape
of the domain, and of a term proportional to the boundary. Therefore, one lowers the kinetic energy of the itinerant particles
by choosing a domain with a small boundary. For the Falicov- Kimball model, this corresponds to having a single “compact”
domain that has no heavy particles.
Received: 21 June 2001 / Accepted: 4 January 2002 相似文献
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Experimental analysis, modeling, and theoretical design of McMaster pore-filled nanofiltration membranes 总被引:1,自引:0,他引:1
A side-by-side comparison of the performance of McMaster pore-filled (MacPF) and commercial nanofiltration (NF) membranes is presented here. The single-salt and multi-component performance of these membranes is studied using experimental data and using a mathematical model. The pseudo two-dimensional model is based on the extended Nernst–Planck equation, a modified Poisson–Boltzmann equation, and hydrodynamic calculations. The model includes four structural properties of the membrane: pore radius, pure water permeability, surface charge density and the ratio of effective membrane thickness to water content. The analysis demonstrates that the rejection and transport mechanisms are the same in the commercial and MacPF membranes with different contributions from each type of mechanism (convection, diffusion and electromigration). Solute rejection in NF membranes is determined primarily by a combination of steric and electrostatic effects. The selectivity of MacPF membranes is primarily determined by electrostatic effects with a significantly smaller contribution of steric effects compared to commercial membranes. Hence, these membranes have the ability to reject ions while remaining highly permeable to low molecular weight organics. Additionally, a new theoretical membrane design approach is presented. This design procedure potentially offers the optimization of NF membrane performance by tailoring the membrane structure and operating variables to the specific process, simultaneously. The procedure is validated at the laboratory scale. 相似文献
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James W. Pavlik Theppawut Israsena Na Ayudhaya Chennagiri R. Pandit Supawan Tantayanon 《Journal of heterocyclic chemistry》2004,41(1):61-67
Trifluromethyl substitution on the pyrazole ring was found to enhance photoreactivity via the P4 pathway which involves interchange of the N2‐C3 ring atoms. Thus, 1‐methyl‐3‐(trifluromethyl)pyrazole (1) and 1‐methyl‐5‐(trifluromethyl)pyrazole (3) transposed with a P4/P6 or P4/P6+P7 ratio of 2.1:1. 1‐methyl‐4‐(trifluromethyl)pyrazole (2) transposed regiospecifically by the P4 transposition pathway. Compounds 2 and 3 were also observed to undergo photocleavage to yield enaminonitrile and enaminoisocyanide products. 相似文献
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J.J. Pan Xiangdong Qiu Kejian Guan Liang Dong FengQing Zhou Wei Wang Mingjie Zhang James Guo Jun Yang Chunmeng Wu 《光学学报》2003,23(Z1)
A low cost, coolerless 980nm diode pumped, gain flattened L band EDFA with fast transient control, high pump efficiency and gain clamping effect was realized by using FBGs as C band seed generators. 相似文献