K(2)CO(3)-mediated reactions of 6-bromo-2-hexenoates and 7-bromo-2-heptenoate with active methylene compounds deliver highly substituted cyclopentane and cyclohexane derivatives, respectively via a sequence of S(N)2-conjugate addition reactions (formal [4 + 1]- and [5 + 1]-annulation) in a diastereoselective manner. 相似文献
We present a new kinetic model describing localized electronic recombination through the excited state of the donor (d) to an acceptor (a) centre in luminescent materials. In contrast to the existing models based on the localized transition model (LTM) of Halperin and Braner (1960 Phys. Rev. 117 408-15) which assumes a fixed d?→?a tunnelling probability for the entire crystal, our model is based on nearest-neighbour recombination within randomly distributed centres. Such a random distribution can occur through the entire volume or within the defect complexes of the dosimeter, and implies that the tunnelling probability varies with the donor-acceptor (d-a) separation distance. We first develop an 'exact kinetic model' that incorporates this variation in tunnelling probabilities, and evolves both in spatial as well as temporal domains. We then develop a simplified one-dimensional, semi-analytical model that evolves only in the temporal domain. An excellent agreement is observed between thermally and optically stimulated luminescence (TL and OSL) results produced from the two models. In comparison to the first-order kinetic behaviour of the LTM of Halperin and Braner (1960 Phys. Rev. 117 408-15), our model results in a highly asymmetric TL peak; this peak can be understood to derive from a continuum of several first-order TL peaks. Our model also shows an extended power law behaviour for OSL (or prompt luminescence), which is expected from localized recombination mechanisms in materials with random distribution of centres. 相似文献
A graph on n vertices is called pancyclic if it contains a cycle of length ? for all 3≤?≤n. In 1972, Erd?s proved that if G is a Hamiltonian graph on n>4k4 vertices with independence number k, then G is pancyclic. He then suggested that n=Ω(k2) should already be enough to guarantee pancyclicity. Improving on his and some other later results, we prove that there exists a constant c such that n>ck7/3 suffices. 相似文献
Treatment of 1-bromo-2,2-dichloro(trimethylsilyl)cyclopropane (2) with tetra--butylammonium fluoride in tetrahydrofuran yields 1-bromo-2-chlorocyclopropene (1). 1H-Cyclopropa[b]phenanthrene (3) can be prepared by aromatization of the Diels-Alder adduct of 1 and 1,2-dimethylene-3,5,6,7,8,9-hexahydronaphthalene (6) using DDQ followed by potassium -butoxide in tetrahydrofuran. 相似文献
In 1955, Arne Pleijel proposed the following problem which remains unsolved to this day: Given a closed plane convex curve C and a point x() at a fixed distance above the plane, as the point x() varies, characterize the point for which the conical surface with vertex x() and base C attains its minimum, and determine the limits as 0 and of this minimum point. The purpose of this paper is to solve the cases where approach its extremities and in the course of the solution, we obtain an interesting characterization of the limit points, which we shall call the Pleijel points of C. A consequence is that the inner Pleijel point provides an upper bound for the isoperimetric defect of C. We also generalize the problem to higher dimensional spaces, and obtain the corresponding characterizations of the limiting points for convex surfaces. 相似文献
1,3,6,8-tetrabenzoylpyrene (1,3,6,8-Bz4PY) and 1,3,6-tribenzoylpyrene (1,3,6-Bz3PY) were synthesized and their crystal structures were determined. The Friedel–Crafts deacylations in PPA of 1,3,6,8-Bz4PY (at 120–200 °C) and of 1,3,6-Bz3PY (at 80–160 °C) have been studied. The mono-deacylation of 1,3,6-Bz3PY was regioselective and led to three dibenzoylpyrenes in the following order of relative amounts: 1,8-Bz2PY > 1,6-Bz2PY > 1,3-Bz2PY. 1,3,6,8-Bz4PY was resistant to deacylation at 120–160 °C. The deacylations of 1,3,6,8-Bz4PY at 200 °C gave the polycyclic aromatic ketone (PAK) 8H-dibenzo[def,qr]chrysen-8-one (DBCO) via an intramolecular Scholl reaction. Two plausible pathways of the Friedel–Crafts deacylation of 1,3,6,8-Bz4PY to give DBCO are proposed. A density functional theory (DFT) B3LYP/6-311(d,p) computational study of the conformational spaces of 1,3,6-Bz3PY and 1,3,6,8-Bz4PY was performed. The estimated energy barriers of formation of dibenzoylpyrenes by deacylation of 1,3,6-Bz3PY increase in the following order: 1,8-Bz2PY < 1,3-Bz2PY < 1,6-Bz2PY. A mechanism of the Friedel–Crafts deacylation of 1,3,6-Bz3PY in PPA via the respective O-protonated ketone and σ-complexes is presented. 相似文献
A disjoint system of type (?, ?, k, n) is a collection ?? = {??1,…, ??m} of pairwise disjoint families of k-subsets of an n-element set satisfying the following condition. For every ordered pair ??i and ??j of distinct members of ?? and for every A ? ??i there exists a B ? ??j that does not intersect A. Let Dn (?, ?, k) denote the maximum possible cardinality of a disjoint system of type (?, ?, k, n). It is shown that for every fixed k ? 2,. This settles a problem of Ahlswede, Cai, and Zhang. Several related problems are considered as well. 相似文献
A simple method which is rigorously invariant under molecular rotations is presented for evaluation of the density functional exchange—correlation energy by numerical quadrature. The corresponding expressions for the first and second derivatives of the energy with respect to nuclear displacement are presented. In particular, such a scheme is necessary to remove the difficulties previously encountered in calculating Kohn—Sham harmonic vibrational frequencies for low-lying modes. 相似文献