1-bromo-2-chlorocyclopropene--A new cycloproparene synthon. Synthesis of 1H-Cyclopropa[b]phenanthrene

Treatment of 1-bromo-2,2-dichloro(trimethylsilyl)cyclopropane (2) with tetra-$\text{n}$-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 $\text{t}$-butoxide in tetrahydrofuran.     

The effect of aryl nitration on gas sorption and permeation in polysulfone

CO_2, CH_4, O_2, and N₂ permeability and solubility of unmodified and aryl-nitrated polysulfone were determined at 35°C and pressures up to 20 atm. The degree of nitration was varied from 0 to 2 nitro groups per repeat unit. The permeability and diffusion coefficients for all gases decreased with increasing degree of nitro substitution. The decrease in gas diffusivity is attributed to a combination of decreased fractional free volume and decreased torsional mobility with increasing degree of substitution. The solubilities of N_2, O_2, and CH₄ do not show a systematic dependence on degree of substitution. However, CO₂ solubility apparently goes through a minimum as the degree of substitution is increased. CO₂ solubility may be influenced by a competition between increases in polymer polarity (favoring higher solubility) and lower free volume (favoring lower solubility) that accompanies increases in the polar nitro substituent concentration. CO₂/CH₄ solubility selectivity increases monotonically as the degree of substitution increases. CO₂/CH₄ permselectivity and diffusivity selectivity increased with increasing degree of substitution. © 1995 John Wiley & Sons, Inc.     

A stabilized column generation scheme for the traveling salesman subtour problem

Given an undirected graph with edge costs and both revenues and weights on the vertices, the traveling salesman subtour problem is to find a subtour that includes a depot vertex, satisfies a knapsack constraint on the vertex weights, and that minimizes edge costs minus vertex revenues along the subtour.We propose a decomposition scheme for this problem. It is inspired by the classic side-constrained 1-tree formulation of the traveling salesman problem, and uses stabilized column generation for the solution of the linear programming relaxation. Further, this decomposition procedure is combined with the addition of variable upper bound (VUB) constraints, which improves the linear programming bound. Furthermore, we present a heuristic procedure for finding feasible subtours from solutions to the column generation problems. An extensive experimental analysis of the behavior of the computational scheme is presented.     

On a problem of A. Pleijel

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.     

Regioselective Friedel–Crafts deacylations of polycyclic aromatic ketones in the pyrene series

1,3,6,8-tetrabenzoylpyrene (1,3,6,8-Bz ₄ PY) and 1,3,6-tribenzoylpyrene (1,3,6-Bz ₃ PY) were synthesized and their crystal structures were determined. The Friedel–Crafts deacylations in PPA of 1,3,6,8-Bz ₄ PY (at 120–200 °C) and of 1,3,6-Bz ₃ PY (at 80–160 °C) have been studied. The mono-deacylation of 1,3,6-Bz ₃ PY was regioselective and led to three dibenzoylpyrenes in the following order of relative amounts: 1,8-Bz ₂ PY > 1,6-Bz ₂ PY > 1,3-Bz ₂ PY. 1,3,6,8-Bz ₄ PY was resistant to deacylation at 120–160 °C. The deacylations of 1,3,6,8-Bz ₄ PY 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-Bz ₄ PY 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-Bz ₃ PY and 1,3,6,8-Bz ₄ PY was performed. The estimated energy barriers of formation of dibenzoylpyrenes by deacylation of 1,3,6-Bz ₃ PY increase in the following order: 1,8-Bz ₂ PY < 1,3-Bz ₂ PY < 1,6-Bz ₂ PY. A mechanism of the Friedel–Crafts deacylation of 1,3,6-Bz ₃ PY in PPA via the respective O-protonated ketone and σ-complexes is presented.     

Disjoint systems

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 D_n (?, ?, 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.     

Ultrafast x-ray diffraction using a streak-camera detector in averaging mode

We demonstrate an apparatus for measuring time-dependent x-ray diffraction. X-ray pulses from a synchrotron are diffracted by a pair of Si(111) crystals and detected with an x-ray streak camera that has single-shot resolution of better than 1 ps. The streak camera is driven by a photoconductive switch, which is triggered by 100-fs laser pulses at a repetition rate of 1 kHz. The laser and the streak camera are synchronized with the synchrotron pulses. In the averaging mode, trigger jitter results in 2-ps temporal resolution. We measured the duration of 5-keV pulses from the Advanced Light Source synchrotron to be 70ps.     

Diamond surface conductivity under atmospheric conditions: theoretical approach

The electron transfer from an H-terminated diamond (100)-2 x 1 surface to a neutral or acidic water adlayer has been theoretically investigated, using quantum mechanical DFT calculations under periodic boundary conditions. A surface conductivity of p-type was found to be induced by the acidic environment. An electron transfer of 1.8 electrons per surface unit cell was observed to take place from the upper part of the diamond valence band to the lowest unoccupied molecular level of the aqueous adlayer that contains one H(3)O(+) ion. The result is a hole delocalized over the whole diamond model slab. Also, a pronounced weakening of the H(3)O(+) bonds by the interaction with the diamond surface is observed.