Batch Delivery Scheduling on a Single Machine

The problem of partitioning a set of independent and simultaneously available jobs into batches and sequencing them for processing on a single machine is presented. Jobs in the same batch are to be delivered together, upon completion of the last job in the batch. Jobs finished before this time have to wait until delivery. There are a delivery cost depending on the number of batches formed and an earliness cost for jobs finished before delivery. The dynamic programming approach to minimizing the total cost is considered, yielding two pseudopolynomial algorithms when the number of batches has a fixed upper bound. A polynomial algorithm for a special case of the problem is also presented.     

Classification of ovoids inPG(3, 32)

A classification of the ovoids inPG(3, 32) is completed with the aid of a computer. The ovoids are examined in terms of which ovals can possibly appear as secant plane sections. A weak necessary condition for two ovals to appear together as plane sections of an ovoid surprisingly turns out to be sufficient to demonstrate that the only possible secant plane sections are translation ovals. A known result regarding ovoids with such plane sections then identifies the ovoids as either elliptic quadrics or Tits ovoids.     

Local error and variable order Adams codes

Error estimates needed for the selection of order in Adams codes are studied in the presence of propagated errors. A new derivation of the Nordsieck form of the Adams methods reveals that codes based on this form have changed order incorrectly and shows how to do it properly.     

The isomers of silacyclopropane

Geometries, relative energies, and electron density distributions in silacyclopropane and five of its isomers are investigated using ab initio methods. VinyIsilane is found to be the most stable isomer, and methyl substitution is preferred at the silicon end of both silaethylene and methyl silylene.     

Cycles of cooperation and free-riding in social systems

Basic evidences on non-profit making and other forms of benevolent-based organizations reveal a rough partition of members between some pure consumers of the public good (free-riders) and benevolent individuals (cooperators). We study the relationship between the community size and the level of cooperation in a simple model where the utility of joining the community is proportional to its size. We assume an idiosyncratic willingness to join the community ; cooperation bears a fixed cost while free-riding bears a (moral) idiosyncratic cost proportional to the fraction of cooperators. We show that the system presents two types of equilibria: fixed points (Nash equilibria) with a mixture of cooperators and free-riders and cycles where the size of the community, as well as the proportion of cooperators and free-riders, vary periodically.     

Theories for network formation in multistage processes

Two different theoretical approaches have been developed to describe network formation in a six-component, three-stage process with the stochastic theory of branching processes. Both approaches make use of probability-generating functions and cascade substitutions. In the POLYM approach, the products of the previous stage, namely, complete (branched) molecules, are used as building units in the subsequent stage. The molar masses and unreacted functionalities are identified by means of dummy variables. In the resulting formulas the sequence of the three stages is clearly visible. In the MONOM approach, the system is treated as a quasi-one-stage process; the original monomers are the building units in all three stages, the sequence of which is only apparent from the input parameters. In the MONOM approach the original monomers are used as building units, irrespective of the stage in which they react. A separate dummy variable is chosen for each possible reaction in each stage in the MONOM approach, so that the two approaches give analytically identical results, but along completely different derivations. This avoids correlation errors in the MONOM approach. Both approaches have incorporated kinetic effects by way of substitution effects in two of the monomers. The two approaches are prefaced by the treatment of several paradigms of increasing complexity to show the unity and strength of the theory and to warn against typical pitfalls.