The moments of the forward recurrence times of an alternating renewal process

Expressions for the moments of the forward recurrence times of an alternating renewal process are presented. The alternating phase-type renewal process is considered in detail.     

Valid inequalities and separation for uncapacitated fixed charge networks

A family of valid linear inequalities for uncapacitated fixed charge networks is given. As special cases this family includes the linear inequalities describing the convex hull of the single-item uncapacitated lot-sizing problem and the variable upper bounds which are typically used in location and distribution planning problems. Various special cases, where the separation problem for the family of inequalities is solvable in polynomial time, are investigated.     

Quantitative analyses of precession diffraction data for a large cell oxide.

Kinematical and two-beam calculations have been conducted and are compared to experimental precession data for the large unit cell crystal La4Cu3MoO12. Precession electron diffraction intensities are found to exhibit approximate two-beam behavior and demonstrate clear advantages over conventional SADP intensities for use in structure solution.     

New access to fluorinated ketoglycolic acid derivatives from trifluoropyruvamides

Hydrates of trifluoropyruvamides are readily obtained from isocyanides and trifluoroacetic anhydride. Under catalysis with secondary amines, these hydrates were successfully reacted with various methylketones to form fluorinated aldol type compounds. The effect of the amine is discussed as well as Henry type additions with nitromethane.     

Far-infrared absorption of large electron-hole drops in stressed Ge

The far-infrared attenuation spectrum due to a large electron-hole drop in inhomogeneously stressed Ge has been measured and compared to the attenuation by small drops in unstressed Ge. The spectrum is analyzed using the full Mie theory for the absorption due to a large sphere; the experimental results are interpreted as bulk plasma absorption in a drop with pair density considerably lowered by the strain.     

A time indexed formulation of non-preemptive single machine scheduling problems

We consider the formulation of non-preemptive single machine scheduling problems using time-indexed variables. This approach leads to very large models, but gives better lower bounds than other mixed integer programming formulations. We derive a variety of valid inequalities, and show the role of constraint aggregation and the knapsack problem with generalised upper bound constraints as a way of generating such inequalities. A cutting plane/branch-and-bound algorithm based on these inequalities has been implemented. Computational experience on small problems with 20/30 jobs and various constraints and objective functions is presented.The research of this author was partially supported by JNICT/INVOTAN under grant No. 30/A/85/PO and by the PAC, contract No. 87/92-106, for computation.     

An elementary survey of general duality theory in mathematical programming

We survey some recent developments in duality theory with the idea of explaining and unifying certain basic duality results in both nonlinear and integer programming. The idea of replacing dual variables (prices) by price functions, suggested by Everett and developed by Gould, is coupled with an appropriate dual problem with the consequence that many of the results resemble those used in linear programming. The dual problem adopted has a (traditional) economic interpretation and dual feasibility then provides a simple alternative to concepts such as conjugate functions or subdifferentials used in the study of optimality. In addition we attempt to make precise the relationship between primal, dual and saddlepoint results in both the traditional Lagrangean and the more general duality theories and to see the implications of passing from prices to price functions. Finally, and perhaps surprisingly, it appears that all the standard algorithms terminate by constructing primal and dual feasible solutions of equal value, i.e., by satisfying generalised optimality conditions.     

Homotopies for computation of fixed points

Given a point to set mapf on a simplex with certain conditions, an algorithm for computing fixed points is described. The algorithm operates by following the fixed point as an initially affine function is deformed towardsf. This research was supported in part by Army Research Office Durham Contract DAHC-04-67-C-0028 and in part by NSF Grant GK-5695.