Stochastic Programming with Recourse: A Modification from an Applications Viewpoint

The paper describes a modified "wait-and-see" approach to solving two-stage stochastic programming problems. The approach, which involves a detailed sensitivity analysis in the classical sense, is described within the frameworks of decision theory and probabilistic programming. Although optimality in the mathematical sense cannot be guaranteed by using the approach, it is suggested that the managerial benefits weigh heavily in its favour. The approach allows management to consider a wide variety of objectives in making the choice between alternatives and facilities detection of the cause of any infeasibility due to management policy constraints. In addition, it allows much simpler programming calculations and provides an upper bound on the benefits that can be obtained by solving the full "here-and-now" problem and thus a judgement of the worth of the added computational burden can easily be made.     

Cycle-maximal triangle-free graphs

We conjecture that the balanced complete bipartite graph _{K⌊n/2⌋,⌈n/2⌉}$K_{\lfloor n/2\rfloor ,\lceil n/2\rceil }$ contains more cycles than any other n$n$-vertex triangle-free graph, and we make some progress toward proving this. We give equivalent conditions for cycle-maximal triangle-free graphs; show bounds on the numbers of cycles in graphs depending on numbers of vertices and edges, girth, and homomorphisms to small fixed graphs; and use the bounds to show that among regular graphs, the conjecture holds. We also consider graphs that are close to being regular, with the minimum and maximum degrees differing by at most a positive integer k$k$. For k=1$k=1$, we show that any such counterexamples have n≤91$n\le 91$ and are not homomorphic to _C5$C_5$; and for any fixed k$k$ there exists a finite upper bound on the number of vertices in a counterexample. Finally, we describe an algorithm for efficiently computing the matrix permanent (a #P$\#P$-complete problem in general) in a special case used by our bounds.     

A Ramsey‐type problem and the Turán numbers*

For each n and k, we examine bounds on the largest number m so that for any k‐coloring of the edges of K_n there exists a copy of K_m whose edges receive at most k?1 colors. We show that for , the largest value of m is asymptotically equal to the Turá number , while for any constant then the largest m is asymptotically larger than that Turá number. © 2002 Wiley Periodicals, Inc. J Graph Theory 40: 120–129, 2002     

Swelling properties and intrinsic reactivities of coal chars produced at elevated pressures and high heating rates

A high-temperature, high-pressure flat-flame burner reactor was developed to prepare char at different pressures. This system achieves particle heating rates of 10⁵ K/s, which better mimics industrial conditions than conventional drop tube or radiative flow reactors. Previous data at atmospheric pressure demonstrated a significant decrease in particle swelling during devolatilization as heating rates increased from 10⁴ K/s (the typical drop tube heating rate) to 10⁵ K/s. Pyrolysis experiments were performed at pressures from 1 to 15 atm at 1300 °C for two bituminous coals and a lignite. Average swelling was determined from a combination of the mass release and the average density. The results indicate significantly lower swelling ratios at elevated pressures than reported in the literature. Scanning electron micrographs show that the bubbles in the bituminous coal particles popped before significant swelling at these elevated heating rates. Lignite particles exhibited shrinkage rather than swelling, but still showed a small effect of pressure. TGA oxidation reactivities were determined for the Pitt #8 and Knife River lignite char samples at their respective char preparation pressures. The oxidation reactivities of both the bituminous and lignite chars decreased with increasing pressure.     

The 5v 3 bands of 18O enriched ozone: line positions of 16O16O18O, 16O18O16O, 16O18O18O and 18O16O18O

The four 5v ₃ bands of ¹⁸O enriched ozone have been observed and analysed for the first time. Two species (¹⁶O¹⁸O¹⁶O and ¹⁸O¹⁶O¹⁸O) belong to the C_2v symmetry group and two other (¹⁸O¹⁸O¹⁶O and ¹⁶O¹⁶O¹⁸O) to the C_s symmetry group. They have been recorded at a resolution of 0.008 cm^?1 with a pathlength of 32.16 m. Despite the very weak absorptions observed, almost 250 energy levels have been derived for each of the 4 species, with J ? 35 and K _a ? 13, and suitable sets of Hamiltonian parameters have been determined. For 3 species it has been necessary to account for the resonance between the (005) and (311) states to correctly reproduce the spectra observed. These resonances, anharmonic for C_2v, and hybrid (both anhar-monic and Coriolis) for C_s symmetry confirm the accidentally extremely strong coupling between the (005) and (311) states for ¹⁶O₃, due in that case to the very close distance between unperturbed energy levels. This work also confirms the excellent prediction of band centres of these four species derived from the recently determined isotopically invariant molecular potential function.     

Cyclic polytopes, hyperplanes, and Gray codes

We consider cyclic d-polytopes P that are realizable with vertices on the moment curve $M_d:t\longrightarrow (t,t^2,\ldots,t^d)$ of order $d\geq 3$. A hyperplane H bisects a j-face of P if H meets its relative interior. For $\ell\geq 1$, we investigate the maximum number of vertices that P can have so that for some $\ell$ hyperplanes, each j-face of P is bisected by one of the hyperplanes. For $\ell > 1$, the problem translates to the existence of certain codes, or equivalently, certain paths on the cube $\{0,1\}^\ell$.