Joint rolling-horizon scheduling of materials processing and lot-sizing with sequence-dependent setups

A lot sizing and scheduling problem from a foundry is considered in which key materials are produced and then transformed into many products on a single machine. A mixed integer programming (MIP) model is developed, taking into account sequence-dependent setup costs and times, and then adapted for rolling horizon use. A relax-and-fix (RF) solution heuristic is proposed and computationally tested against a high-performance MIP solver. Three variants of local search are also developed to improve the RF method and tested. Finally the solutions are compared with those currently practiced at the foundry.     

Some Special Pairs of Σ2 e-Degrees

It is shown that there are incomparable Σ₂ e-degrees a, b such that every e-degree strictly less than a is also less than b .     

On countable homogeneous 3-hypergraphs

Summary We present some results on countable homogeneous 3-hypergraphs. In particular, we show that there is no unexpected homogeneous 3-hypergraph determined by a single constraint.The authors are grateful for support from NSERC (Canada) Grant A3040     

Formal Hecke algebras and algebraic oriented cohomology theories

In the present paper, we generalize the construction of the nil Hecke ring of Kostant–Kumar to the context of an arbitrary formal group law, in particular, to an arbitrary algebraic oriented cohomology theory of Levine–Morel and Panin–Smirnov (e.g., to Chow groups, Grothendieck’s \(K_0\) , connective \(K\) -theory, elliptic cohomology, and algebraic cobordism). The resulting object, which we call a formal (affine) Demazure algebra, is parameterized by a one-dimensional commutative formal group law and has the following important property: specialization to the additive and multiplicative periodic formal group laws yields completions of the nil Hecke and the 0-Hecke rings, respectively. We also introduce a formal (affine) Hecke algebra. We show that the specialization of the formal (affine) Hecke algebra to the additive and multiplicative periodic formal group laws gives completions of the degenerate (affine) Hecke algebra and the usual (affine) Hecke algebra, respectively. We show that all formal affine Demazure algebras (and all formal affine Hecke algebras) become isomorphic over certain coefficient rings, proving an analogue of a result of Lusztig.     

Pinnatoxin H: a new pinnatoxin analogue from a South China Sea Vulcanodinium rugosum isolate

Pinnatoxin H was isolated from a culture of the dinoflagellate Vulcanodinium rugosum isolated from the South China Sea. The structure of pinnatoxin H was elucidated by LC–MS/MS and NMR spectroscopy. It was found to have the same macrocyclic structure and substituents as pinnatoxins D, E and F, but the side chain on the cyclohexenyl ring was an ethenyl group, as found in pinnatoxin G and portimine. The observation that this strain of V. rugosum produced only pinnatoxin H and portimine is consistent with previous findings that the profile of pinnatoxins can vary significantly among strains. The acute toxicity of pinnatoxin H to mice was 67 μg/kg (intraperitoneal) and 163 μg/kg (gavage).     

The Effect of Viscosity Ratio and Peclet Number on Miscible Viscous Fingering in a Hele-Shaw Cell: A Combined Numerical and Experimental Study

Transport in Porous Media - The results from a series of well characterised, unstable, miscible displacement experiments in a Hele-Shaw cell with a quarter five-spot source-sink geometry are...     

Fast mixing for independent sets,colorings, and other models on trees

We study the mixing time of the Glauber dynamics for general spin systems on the regular tree, including the Ising model, the hard‐core model (independent sets), and the antiferromagnetic Potts model at zero temperature (colorings). We generalize a framework, developed in our recent paper (Martinelli, Sinclair, and Weitz, Tech. Report UCB//CSD‐03‐1256, Dept. of EECS, UC Berkeley, July 2003) in the context of the Ising model, for establishing mixing time O(nlog n), which ties this property closely to phase transitions in the underlying model. We use this framework to obtain rapid mixing results for several models over a significantly wider range of parameter values than previously known, including situations in which the mixing time is strongly dependent on the boundary condition. We also discuss applications of our framework to reconstruction problems on trees. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007     

A kinetic and mechanistic study of the formation of alkyl nitrates in the photo-oxidation of n-heptane studied under atmospheric conditions

The photo-oxidation of n-heptane in synthetic air containing methyl nitrite and nitric oxide has been ivestigated in an atmospheric flow reactor. By measuring the total yields of heptyl nitrate products, relative to the depletion of the n-heptane, the rate constant ratio, k_3b/k_3a has been determined for the reactions: (1) Over the temperature range 253–325 K and at a total pressure of 730 Torr, the following relative Arrhenius equation has been obtained from the present study together with literature data: These results confirm that the formation of alkyl nitrates from the photo-oxidation of n-alkanes arise from a primary reaction between the alkylperoxy radicals and nitric oxide. Furthermore the present experiments show that the lifetime of the intermediate in this type of reaction, presumed to be an alkyl peroxynitrite, ROONO, must be less than a few seconds.