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31.
The adsorption of chlorobenzene on Si(111)7 × 7 at room temperature was studied by scanning tunneling microscopy (STM). Selective chemisorption was observed at different adatom sites. It was found that the center adatoms were more reactive than the corner adatoms, and the faulted half of the unit cell was more reactive than the unfaulted. The mechanism is discussed in terms of the electronic and atomic structures in Si(111)7 × 7. Both preferences indicate that chlorobenzene was present initially in a mobile precursor state. 相似文献
32.
Colin Rogers 《Journal of Nonlinear Mathematical Physics》2019,26(1):98-106
Here, a recently introduced nine-body problem is shown to be decomposable via a novel class of reciprocal transformations into a set of integrable Ermakov systems. This Ermakov decomposition is exploited to construct more general integrable nine-body systems in which the canonical nine-body system is embedded. 相似文献
33.
An electron spectroscopic investigation of the interaction of methanol with polycrystalline aluminum
X-ray and ultraviolet photoelectron spectroscopic results are reported for the interaction of CH3OH with clean polycrystalline Al in the temperature range 110–500 K. Methanol is moleculary chemisorbed at low exposure and low temperature (110 K) followed by condensation at higher exposure. Bonding mechanisms and geometries in the condensed and chemisorbed layers are discussed. The multilayers desorb beginning near 170 K and the chemisorbed layer is converted into a surface methoxide. Room temperature adsorption also leads to formation of the methoxide species which is stable to ~500 K, at which point it decomposes evolving CH4 and leaves the surface oxidized. 相似文献
34.
This study applies the theory of stochastic processes to the equilibrium statistical physics of polymers in solution. The topics treated include random copolymers and randomly branching polymers, with self-consistent mean field effects. A new and more natural way of dealing with Boltzmann weighting is discussed, which makes it possible from the beginning of a calculation to consider only the physical polymer conformations. We also show that in general the random copolymer problem can be reduced to the ordinary polymer problem, and treat the self-consistent field problem for a general branching polymer. 相似文献
35.
36.
Leo Rogers 《Research in Mathematics Education》2013,15(1):225-240
Reference to the history of mathematics has been widely used in discussions of the development of curricula, the problems students have in learning mathematics, and the development of concepts in the individual. This paper examines the background to the "Biogenetic Law" [1] which has influenced so much thinking in educational theory, and the use of the "principle of parallelism" where individual development is claimed to mirror the historical development of the subject matter. Interpretations of the history of mathematics which are used to justify these claims are examined, and the universality of the supposed concepts is challenged. Questions are raised about some of the fundamental tenets of Piagetian epistemology. 相似文献
37.
Christopher L. Rogers 《Letters in Mathematical Physics》2012,100(1):29-50
A manifold is multisymplectic, or more specifically n-plectic, if it is equipped with a closed nondegenerate differential form of degree n + 1. In previous work with Baez and Hoffnung, we described how the ‘higher analogs’ of the algebraic and geometric structures
found in symplectic geometry should naturally arise in 2-plectic geometry. In particular, just as a symplectic manifold gives
a Poisson algebra of functions, any 2-plectic manifold gives a Lie 2-algebra of 1-forms and functions. Lie n-algebras are examples of L
∞-algebras: graded vector spaces equipped with a collection of skew-symmetric multi-brackets that satisfy a generalized Jacobi
identity. Here, we generalize our previous result. Given an n-plectic manifold, we explicitly construct a corresponding Lie n-algebra on a complex consisting of differential forms whose multi-brackets are specified by the n-plectic structure. We also show that any n-plectic manifold gives rise to another kind of algebraic structure known as a differential graded Leibniz algebra. We conclude
by describing the similarities between these two structures within the context of an open problem in the theory of strongly
homotopy algebras. We also mention a possible connection with the work of Barnich, Fulp, Lada, and Stasheff on the Gelfand–Dickey–Dorfman
formalism. 相似文献
38.
L. C. G. Rogers 《Mathematics and Financial Economics》2009,2(3):151-171
The theory of risk measurement has been extensively developed over the past ten years or so, but there has been comparatively
little effort devoted to using this theory to inform portfolio choice. One theme of this paper is to study how an investor
in a conventional log-Brownian market would invest to optimize expected utility of terminal wealth, when subjected to a bound
on his risk, as measured by a coherent law-invariant risk measure. Results of Kusuoka lead to remarkably complete expressions
for the solution to this problem. The second theme of the paper is to discuss how one would actually manage (not just measure)
risk. We study a principal/agent problem, where the principal is required to satisfy some risk constraint. The principal proposes
a compensation package to the agent, who then optimises selfishly ignoring the risk constraint. The principal can pick a compensation
package that induces the agent to select the principal’s optimal choice. 相似文献
39.
40.
Richard A. Bunce David Rogers Takahiro Nago Scott A. Bryant 《Journal of heterocyclic chemistry》2008,45(2):547-550
Treatment of 2‐fluoro‐5‐nitrobenzyl bromide with active methylene compounds in the presence of excess potassium carbonate in acetone leads to the formation of highly functionalized 4H‐1‐benzopyrans by a tandem SN2‐SNAr reaction sequence. The reaction works well with β‐keto esters, β‐keto sulfones, β‐keto phosphine oxides, β‐keto phosphonates and β‐keto nitriles. The reaction is simple to perform and affords products in 50‐92% yields. 相似文献