Numerical Modeling of Solitons in a Low Birefringent Optical Fiber

A numerical investigation, based on the split-step Fourier transform algorithm of all optical switching of solitons in a low birefringent optical fiber is presented. The numerical algorithm is described in detail. This revised version was published online in August 2006 with corrections to the Cover Date.     

Syntheses of 5‐alkylthio‐1,3‐diaryl‐1,2,4‐triazoles

Arylation of the readily available 3‐alkythio‐5‐aryl‐1,2,4‐triazoles gave 5‐alkylthio‐1,3‐diaryl‐1,2,4‐triazoles in moderate yield. The structures of the latter were confirmed by NOE and ¹³C‐NMR.     

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.     

Titanium(IV) tungstosilicate and titanium(IV) tungstophosphate: two new inorganic ion exchangers

Crystalline phases of Ti(IV) tungstosilicate and Ti(IV) tungstophosphate have been synthesised. The ion-exchange capacities of Ti(IV) tungstosilicate and Ti(IV) tungstophosphate have been reported as 0.44 and 0.80 mequiv./g, respectively. Both materials show monofunctional ion-exchange characteristic and are stable in 0.1 M solutions of HNO3, HCl, H2SO4 and acetone and benzene. Ti(IV) tungstosilicate is found to be more stable thermally than Ti(IV) tungstophosphate (loss in ion-exchange capacity was found as 58 and 80%, respectively for samples heated at 200 degrees C). The Kd values for heavy metals such as Pb, Hg, Cd, Sb, Co, Zn, Ni, Fe, Cr etc. have been reported in demineralised water and two surfactant media by batch processes. Cr3+, Fe3+ and Sn4+ are totally adsorbed on both the materials in demineralised water while a decrease in Kd value with increase in concentration of two surfactants is reported. On the basis of Kd values for metal ions, thirteen binary separations and five ternary separations on Ti(IV) tungstosilicate and thirteen different binary separations and four different ternary separations on Ti(IV) tungstophosphate have been achieved. Separation of methylamine from ethylamine has been done by GC on a column packed with Ti(IV) tungstophosphate.