CCSD(T) and B3LYP calculations were done on 1H-, 2H-, and 3H-pyrroles, phospholes, and siloles to account for the relative stabilities, activation energies for sigmatropic hydrogen shifts, and Diels−Alder reactivities with two model dienophiles. The computed barrier heights for sigmatropic rearrangements in phospholes account for the observed reversible equilibrium at higher temperatures. Both CCSD(T) and B3LYP calculations support the experimental observation that 1H- and 2H-phospholes lead to the Diels−Alder adduct of 2H-phosphole and validate Mathey's proposal that 1H-phosphole (1P) converts to 2H-phosphole (2P) prior to the participation in the Diels−Alder reactions. In contrast to what is observed in phospholes, the sigmatropic shifts in pyrroles and siloles require higher activation energies compared to the Diels−Alder reactions, which indicate no sigmatropic shifts prior to cycloadditions. Distortion energies of dienophiles explain the small discrepancy between the activation energies and exothermicities in the reactions involving ethylene and acetylene. The frontier molecular orbital (FMO) analysis and the extent of charge transfer values from diene to dienophile are also used to assess the Diels−Alder reactivities of all of the dienes considered in this study.

This paper presents a new approach to the tolerance synthesis of the component parts of assemblies by simultaneously optimizing three manufacturing parameters: manufacturing cost, including tolerance cost and quality loss cost; machining time; and machine overhead/idle time cost. A methodology has been developed using the Genetic Algorithm (GA) technique to solve this multiobjective optimization problem. The effectiveness of the proposed methodology has been demonstrated by solving a wheel mounting assembly problem consisting of five components, two subassemblies, two critical dimensions, two functional tolerances, and eight operations. Significant cost saving can be achieved by employing this methodology.

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Equilibrium geometries and the relative stabilities of 1H‐, 2H‐ and 3H‐phospholes and their methyl‐ and vinyl‐substituted analogs were computed at the B3LYP/6–31G* level. The transition states and products were located for the Diels–Alder reactions of all the dienes with ethylene. The effect of substitution on the geometries, relative stabilities and Diels–Alder reactivities of 1H‐, 2H‐ and 3H‐phospholes were analyzed. The relative stabilities predict that the substitution on phospholes prefers phosphorus over carbon. Computations show that the activation energies are not altered much by substitution of either methyl or vinyl groups on phospholes, but most of the substituted phospholes require slightly higher activation energies than the corresponding parent phospholes. 2H‐phospholes require lower activation energies than 1H‐ and 3H‐phospholes. The reactivity ordering based on FMO energy gaps and the activation energies are similar and follows the sequence 2H‐ > 3H‐ > 1H‐phospholes. The quantaum of charge‐transfer values from diene to dienophile at the transition states and distortion energies were calculated. Copyright © 2003 John Wiley & Sons, Ltd.

Traditionally, tolerance allocation and scheduling have been dealt with separately in the literature. The aim of tolerance allocation is to minimize the tolerance cost. When scheduling the sequence of product operations, the goal is to minimize the makespan, mean flow time, machine idle time, and machine idle time cost. Calculations of manufacturing costs derived separately using tolerance allocation and scheduling separately will not be accurate. Hence, in this work, component tolerance was allocated by minimizing both the manufacturing cost (sum of the tolerance and quality loss cost) and the machine idle time cost, considering the product sequence. A genetic algorithm (GA) was developed for allocating the tolerance of the components and determining the best product sequence of the scheduling. To illustrate the effectiveness of the proposed method, the results are compared with those obtained with existing wheel mounting assembly discussed in the literature.