On the equitability of multiply-connected monolayered cyclofusene

Multiply-connected monolayered cyclofusene (MMC) is a fused hexacyclic system with an exterior region and at least two interior empty regions called holes, as in figure 1. Each hexacyle has either: (a) two edges belonging to an exterior boundary and at least one hole, or (b) two edges belonging to boundaries of at least two holes. Let G be the graph of a given MMC. We show that G is equitable if and only if the set of vertices belonging to three hexacycles is equitable.     

A tabu search heuristic for solving the CLSP with backlogging and set-up carry-over

In this paper, the multi-item, single-level, capacitated, dynamic lot sizing problem with set-up carry-over and backlogging, abbreviated to CLSP⁺, is considered. The problem is formulated as a mixed integer programming problem. A heuristic method consisting of four elements: (1) a demand shifting rule, (2) lot size determination rules, (3) checking feasibility conditions and (4) set-up carry-over determination, provides us with an initial feasible solution. The resulting feasible solution is improved by adopting the corresponding set-up and set-up carry-over schedule and re-optimizing it by solving a minimum-cost network flow problem. Then the improved solution is used as a starting solution for a tabu search procedure, with the value of moves assessed using the same minimum-cost network problem. Computational results on randomly generated problems show that the algorithm, which is coded in C++, is able to provide optimal solutions or solutions extremely close to optimal. The computational efficiency makes it possible to solve reasonably large problem instances routinely on a personal computer.     

A facile synthesis of new 3-(2-benzimidazolyl)-2-alkyl-4-(3H)-quinazolinones under microwave irradiation

Preparation of 2-amino-N-(1-H-benzimidazol-2-yl)benzamide and a variety of new 3-(2-benzimidazolyl)-2-alkyl-4-(3H)-quinazolinones using isatoic anhydride, 2-aminobenzimidazole and orthoesters under microwave irradiation are described.     

SnCl4 and SbCl5 promoted aromatization of enamines

Aromatic amines have been synthesized efficiently from enamines using SnCl₄ and SbCl₅ in CH₂Cl₂ at room temperature.     

Asymmetric intermolecular C-H activation,using immobilized dirhodium tetrakis((S)-N-(dodecylbenzenesulfonyl)- prolinate) as a recoverable catalyst

[reaction: see text] Heterogenization of dirhodium tetrakis((S)-N-dodecylbenzenesulfonyl)prolinate) (Rh(2)(S-DOSP)(4)) can be readily achieved on a pyridine functionalized highly cross-linked polystyrene resin. The immobilized complex is readily recycled and exhibits excellent catalytic activity for asymmetric intermolecular C-H activation by means of rhodium carbenoid induced C-H insertion.     

An efficient procedure for the synthesis of coumarin derivatives using TiCl4 as catalyst under solvent-free conditions

The ability of titanium(IV) chloride as a catalyst to promote the Pechmann condensation reaction with a range of phenols and β-keto esters is described.The reaction was carried out by addition of TiCl₄ to a mixture of the phenol and the β-keto ester with thorough stirring in the absence of a solvent and represents an improvement on the classical Pechmann conditions. The yields of coumarins obtained via this novel protocol were significantly higher than those using the conventional method and the reaction duration was reduced to a few minutes or even a few seconds.     

Characterization of aerogel prepared high-surface-area alumina: in situ FTIR study of dehydroxylation and pyridine adsorption

Mesoporous high-surface-area alumina was prepared by a modified aerogel procedure. Specific surface areas between 530-685 m(2)g(-1) were obtained after heat treatment at 500 degrees C. Nitrogen adsorption studies have shown that surface areas and pore characteristics change upon decomposition of aluminum hydroxide to oxide as well as upon compaction of oxide powders. The surface area of aluminum hydroxide increased to a maximum, while the pore volume and diameter decreased as the hydroxide was heated to a temperature of 400 degrees C. Heating at higher temperatures resulted in sintering of the particles accompanied by a decline in the surface area. Compaction of activated alumina into pellets was accompanied by a relatively gradual change in the surface area and pore characteristics at pressures below 6.9 x 10(7) Pa, while severe changes took place at a pressure of 1.4 x 10(8) Pa. In situ IR studies of the dehydroxylation of the alumina surface, showed nu(OH) absorptions for isolated surface hydroxy groups centering at 3670, 3714, and 3765 cm(-1), which are shifted to lower frequencies than common literature values. Pyridine was found to adsorb on Al(3+) ions as well as through hydrogen bonding to relatively acidic surface OH groups, and IR spectra indicated the presence of strong Lewis acid sites.