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81.
Rosenau T Ebner G Stanger A Perl S Nuri L 《Chemistry (Weinheim an der Bergstrasse, Germany)》2004,11(1):280-287
The regioselectivity of the oxidation of alpha-tocopherol (the main component of vitamin E) to an ortho-quinone methide (oQM) has been explained in the literature mostly by the ill-defined term "Mills-Nixon effect". In this paper we describe the preparation of eleven alpha-tocopherol derivatives, different from each other by the sum of annulation angles, but keeping the electronic factors unchanged. These compounds underwent Ag(2)O oxidation, forming two isomeric oQMs that were trapped by vinylmethyl ether. It was found that the isomeric product ratio changes smoothly as a function of the annulation angles, not abruptly from one regioisomer to the other on going from five- to six- and seven-membered rings, as predicted by the Mills-Nixon effect. The relative amounts of the products were determined at four different temperatures, and assuming that the product ratio represents the relative rates ratio, the relative enthalpy of activations could be obtained. Theoretically (at B3LYP/6-31G* theoretical level) four different intermediates were considered. Each of these underwent angular angles deformations to model the two regioisomers. At each deformation angle the energy difference between the two intermediates models was correlated to the experimental data for each of the four intermediates. It was found that the angle-deformed lithium (6-methyl-2-benzylium)phenolate correlated best (R>0.994) to the experimental data. This study confirms that the regioselectivity of the two isomeric oQMs in the oxidation of alpha-tocopherol and related compounds is simply a function of angular strain, best explained by the SIBL (strain-induced bond localization) model. In addition, this study provides evidence that the highest energy intermediate in the oxidation of vitamin E is a phenolate-benzyl cation. 相似文献
82.
The Derived Picard Group is a Locally Algebraic Group 总被引:1,自引:0,他引:1
Amnon Yekutieli 《Algebras and Representation Theory》2004,7(1):53-57
Let A be a finite-dimensional algebra over an algebraically closed field K. The derived Picard group DPic
K
(A) is the group of two-sided tilting complexes over A modulo isomorphism. We prove that DPic
K
(A) is a locally algebraic group, and its identity component is Out0
K
(A). If B is a derived Morita equivalent algebra then DPic
K
(A)DPic
K
(B) as locally algebraic groups. Our results extend, and are based on, work of Huisgen-Zimmermann, Saorín and Rouquier. 相似文献
83.
84.
When suitably rescaled, the distribution of the angular gaps between branches of off-lattice radial diffusion-limited aggregation is shown to approach a size-independent limit. The power-law expected from an asymptotic fractal dimension D = 1.71 arises only for very small angular gaps, which occur only for clusters significantly larger than M = 10(6) particles. Intermediate size gaps exhibit an effective dimension around 1.67, even for M--> infinity. They dominate the distribution for clusters with M<10(6). The largest gap approaches a finite limit extremely slowly, with a correction of order M(-0.17). 相似文献
85.
The propagation of an optical pulse in a coupled-resonator optical waveguide may be calculated nonperturbatively to all orders of dispersion, in the conventional tight-binding approximation, even though the dispersion relationship is nonlinear. Working in this framework, we discuss limits of the physical parameters and approximations to the exact formulation that highlight the conditions under which pulse distortion can be minimized. The results are fundamental to the design of coupled-resonator optical waveguides and are also relevant to other applications of the tight-binding method. 相似文献
86.
Let
be a triangulated category with coproducts,
the full subcategory of compact objects in
. If
is the homotopy category of spectra, Adams (Topology 10 (1971) 185–198), proved the following: All homological functors
are the restrictions of representable functors on
, and all natural transformations are the restrictions of morphisms in
. It has been something of a mystery, to what extent this generalises to other triangulated categories. In Neeman (Topology 36 (1997) 619–645), it was proved that Adams’ theorem remains true as long as
is countable, but can fail in general. The failure exhibited was that there can be natural transformations not arising from maps in
. A puzzling open problem remained: Is every homological functor the restriction of a representable functor on
? In a recent paper, Beligiannis (Relative homological and purity in triangulated categories, 1999, preprint) made some progress. But in this article, we settle the problem. The answer is no. There are examples of derived categories
of rings, and homological functors
which are not restrictions of representables. 相似文献
87.
We prove the additivity theorem for the K-theory of triangulated derivators. This solves one of the conjectures made by Maltsiniotis in [G. Maltsiniotis, La K-théorie d'un dérivateur triangulé, in: Alexei Davydov, Michael Batanin, Michael Johnson, Stephen Lack, Amnon Neeman (Eds.), Categories in Algebra, Geometry and Physics, Conference and Workshop in honor of Ross Street's 60th Birthday, in: Contemp. Math., vol. 431, Amer. Math. Soc., 2007, pp. 341-368]. We also review some basic definitions and results in the theory of derivators in the sense of Grothendieck. 相似文献
88.
89.
Amnon Rosenmann 《Israel Journal of Mathematics》1997,99(1):285-313
Given a presentation of ann-generated group, we define the normalized cyclomatic quotient (NCQ) of it, which gives a number between 1−n and 1. It is computed through an investigation of the asymptotic behavior of a kind of an “average rank”, or more precisely
the quotient of the rank of the fundamental group of a finite subgraph of the corresponding Cayley graph by the size of the
subgraph. In many ways (but not always) the NCQ behaves similarly to the behavior of the spectral radius of a symmetric random
walk on the graph. In particular, it characterizes amenable groups. For some types of groups, like finite, amenable or free
groups, its value equals that of the Euler characteristic of the group. We give bounds for the value of the NCQ for factor
groups and subgroups, and formulas for its value on direct and free products. Some other asymptotic invariants are also discussed. 相似文献
90.
Stanger A 《The journal of physical chemistry. A》2008,112(50):12849-12854
Localized benzene derivatives can be separated into two classes, one that retains large diamagnetic ring currents and a second that loses the diamagnetic ring current. Energetic criteria and NICS scan are used to evaluate the nature of the two classes. Hückel-type treatment, MO analysis, and comparison to model compounds suggest that there is no connection between geometric localization and the loss of aromaticity. 相似文献