On degenerate multi-row Gomory cuts

Borozan and Cornuéjols show that valid inequalities for an infinite relaxation for MIPs, relative to some vertex f of the linear relaxation, are determined by maximal lattice-free convex sets containing f. We show that cuts for the original MIP are given by such sets with f in the interior.     

A counterexample to a conjecture of Gomory and Johnson

In Mathematical Programming 2003, Gomory and Johnson conjecture that the facets of the infinite group problem are always generated by piecewise linear functions. In this paper we give an example showing that the Gomory-Johnson conjecture is false.     

Copolymerization of styrene with (Z)-1,3-pentadiene in the presence of a syndiotactic-specific catalyst

Copolymerization of styrene with (Z)-1,3-pentadiene affords copolymers mostly containing 1,2 pentadiene units. Both the styrene and the pentadiene units are in syndiotactic arrangement but the comonomer sequence distribution is far from bernoullian. Interestingly, the behavior of (Z)-1,3-pentadiene does not change much when polymerization temperature raises from −20 to +20°C, notwithstanding that (Z)-1,3-pentadiene affords a 1,2-syndiotactic homopolymer at −20°C but a prevailingly 1,4 cis homopolymer at +20°C. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 2697–2702, 1997     

Properties of solution-grown crystals of fractions of isotactic polypropylene with different degrees of stereoregularity

Solution-grown crystals of fractions of isotactic polypropylene (IPP) with different degrees of stereoregularity have been obtained by isothermal crystallization from α-chloronaphthalene, using a self-seeding technique. Electron micrographs of samples, crystallized under the same undercooling, show that, with decreasing fraction of isotactic pentads, the perfect rectangular shape of the single crystal is lost and the presence of more complex morphologies is increasingly observed. The equilibrium dissolution temperature T_d of IPP fractions, from polymers prepared with a titanium based catalyst, decreases linearly with decreasing percentage of isotactic pentads. An extrapolated value of 171°C is obtained for the equilibrium dissolution temperature of a crystal of IPP with 100% isotactic pentads, i.e., an IPP crystal free of configurational defects. The melting temperature T′_m and the apparent enthalpy of fusion ΔH of crystallized and annealed crystal aggregates have been determined by differential calorimetry. The equilibrium melting temperature T_m also depends greatly upon the isotactic pentad concentration. For 100% concentration the extrapolated value of T_m is 181°C. T_m decreases about 1°C per 1% decrease in the isotactic pentad population. The observed equilibrium melting and dissolution temperature depression does not follow the predictions of the Flory equation for copolymer crystallization. In fact, the effect of decreasing probability of isotactic sequence propagation is to depress T_d and T_m much more rapidly. The apparent enthalpy of fusion of both solution-grown crystals and melt-recrystallized samples decreases with an increase in the number of configurational impurities along the chain. For the most stereoregular fraction the average length of isotactic stereoblocks has been compared with the lamellar thickness of solution-grown lath-shaped single crystals.