A generic view of Dantzig-Wolfe decomposition in mixed integer programming

The Dantzig-Wolfe reformulation principle is presented based on the concept of generating sets. The use of generating sets allows for an easy extension to mixed integer programming. Moreover, it provides a unifying framework for viewing various column generation practices, such as relaxing or tightening the column generation subproblem and introducing stabilization techniques.     

Chromatic polynomial, q-binomial counting and colored Jones function

We define a q-chromatic function and q-dichromate on graphs and compare it with existing graph functions. Then we study in more detail the class of general chordal graphs. This is partly motivated by the graph isomorphism problem. Finally we relate the q-chromatic function to the colored Jones function of knots. This leads to a curious expression of the colored Jones function of a knot diagram K as a chromatic operator applied to a power series whose coefficients are linear combinations of long chord diagrams. Chromatic operators are directly related to weight systems by the work of Chmutov, Duzhin, Lando and Noble, Welsh.     

Quantitative Comparison of REAPDOR and TRAPDOR Experiments by Numerical Simulations and Determination of H–Al Distances in Zeolites

Quantitative H–Al distances in acid sites of two zeolites with MFI and IFR framework topology were obtained by numerical simulation of ¹H{²⁷Al} rotational echo adiabatic passage double resonance (REAPDOR) experiments. A ²⁷Al offset-dependent data set yields for each resolved ¹H NMR line a corresponding nuclear electric quadrupole coupling constant of the neighboring ²⁷Al site. This information is used for analyzing a second data set for on-resonance irradiation, where the dipolar evolution time (number of rotor cycles) was varied, to yield the ¹H–²⁷Al dipolar coupling constant. Numerical simulations indicate that the REAPDOR method does not depend significantly on the polar angles, defining the orientation of the electric field gradient tensor of ²⁷Al with respect to the Al–H dipolar vector. In contrast, the transfer of populations in double resonance sequence is sensitive to these angles, and it can be thus used to measure them.     

Bubble point pressure estimates from Gibbs ensemble simulations

Bubble pressure points of ethanol–1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea refrigerant) mixtures from the third Industrial Fluid Properties Simulation Challenge are computed using publicly available molecular simulation software. Several published force fields are compared against the known answers provided in the contest guidelines and the best force fields are used to make predictions for the unknown results.     

Spectral Properties of Four-Dimensional Compact Flat Manifolds

We study the spectral properties of a large class of compact flat Riemannian manifolds of dimension 4, namely, those whose corresponding Bieberbach groups have the canonical lattice as translation lattice. By using the explicit expression of the heat trace of the Laplacian acting on p-forms, we determine all p-isospectral and L-isospectral pairs and we show that in this class of manifolds, isospectrality on functions and isospectrality on p-forms for all values of p are equivalent to each other. The list shows for any p, 1 ≤ p ≤ 3, many p-isospectral pairs that are not isospectral on functions and have different lengths of closed geodesics. We also determine all length isospectral pairs (i.e. with the same length multiplicities), showing that there are two weak length isospectral pairs that are not length isospectral, and many pairs, p-isospectral for all p and not length isospectral. Mathematics Subject Classifications (2000): 58J53, 58C22, 20H15.     

Recent changes in A-level Mathematics: is the availability and uptake of mechanics declining yet more?

In the past 6 years changes have occurred in GCE A-levels. Inparticular, there have been several major changes in A-levelMathematics courses. As engineering students are usually requiredto have studied A-level Mathematics, or its equivalent, thesechanges have had an effect on their prior mathematical knowledge.Moreover, engineering students traditionally obtained a goodgrounding in mechanics as part of their A-level Mathematicsqualification. However, mechanics, which was once included inthe core syllabus, is now optional. This article investigatesthe current availability and uptake of mechanics modules withinA-level Mathematics courses in schools. Comparisons are drawnbetween these results and results of a survey of schools in2004 and surveys of first year engineering students conductedin 2004 and 2005. It is found that there is a decline in theavailability of mechanics modules and the uptake of more thanone mechanics module has also decreased. The implications ofthese findings for engineering educators are discussed.     

Novel acrylic macromonomer with amphiphilic character derived from Triton X‐100: Radical copolymerization with methyl methacrylate and thermal properties

This article explores the synthesis of a novel methacrylic macromonomer with an amphiphilic character derived from poly(ethylene glycol) tert‐octylphenyl ether (MT) and its respective homopolymer. To know their reactivity in radical copolymerization reactions with methyl methacrylate (MMA), a model monomer (MTm) was synthesized to determine the reactivity ratios and compare them with the low molar fractions of copolymers of MT with MMA because they were difficult to isolate. They were r_MTm = 0.97 and r_MMA = 0.95. The compositional diagrams when representing the weight fraction of MT and MTm in the feed and the copolymer suggested that a clear correlation exists between the experimental points of the model monomer MTm and the macromonomer MT ones, suggesting that the length of the side poly(ethylene oxide) chain does not affect the reactivity of the methacrylic double bond in the prepared monomers for this type of polymerization reaction. The reactivity ratios of the copolymers have a tendency for the formation of random or Bernoullian copolymers. The glass‐transition temperatures (T_g's) of the prepared copolymers were determined by differential scanning calorimetry, deviated from the Fox equation, and discussed on the basis of treatments that consider the influence of the monomeric units along the copolymer chains, determining the T_g of the corresponding alternating dyads. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1641–1649, 2003