Control of off-flavor compounds in aluminum can production

Aluminum cans have intermittently been associated with the development of off-flavors in beverages. Certain organic compounds, e.g., aldehydes and ketones, are known to contribute to flavor defects; trans-2-nonenal can be detected at 0.1 μg l^?1 levels by trained tasters. In a recent study, the production process used to form two-piece aluminum cans was examined. Samples of aluminum coil stock, partly formed cans and finished cans were obtained from typical production lins and examined by a flavor panel and by chromatographic and spectroscopic methods in an effort to develop routine techniques for monitoring can production. Capillary-column gas chromatography and, after derivatization with dinitrophenylhydrazone, high-performance liquid chromatography are useful for quantifying off-flavor compounds and precursors in lubricants and other materials used in rolling mills and can-making operations, but are not adaptable to on-line monitoring. Correlations between gas-chromatographic data and flavor panel assessments were good.     

Toward high-performance computational chemistry: I. Scalable Fock matrix construction algorithms

Several parallel algorithms for Fock matrix construction are described. The algorithms calculate only the unique integrals, distribute the Fock and density matrices over the processors of a massively parallel computer, use blocking techniques to construct the distributed data structures, and use clustering techniques on each processor to maximize data reuse. Algorithms based on both square and row-blocked distributions of the Fock and density matrices are described and evaluated. Variants of the algorithms are discussed that use either triple-sort or canonical ordering of integrals, and dynamic or static task clustering schemes. The algorithms are shown to adapt to screening, with communication volume scaling down with computation costs. Modeling techniques are used to characterize algorithm performance. Given the characteristics of existing massively parallel computers, all the algorithms are shown to be highly efficient for problems of moderate size. The algorithms using the row-blocked data distribution are the most efficient. © 1996 by John Wiley & Sons, Inc.     

Intramolecular behaviors of anthryldicarbenic systems: dibenzo[b,f]pentalene and 1H,5H-dicyclobuta[de,kl]anthracene

9,10-Bis[methoxy(trimethylsilyl)methyl]anthracenes (24), synthesized from 9,10-dilithioanthracene (26) and bromomethoxytrimethylsilylmethane (27, 2 equiv), decompose (550-650 degrees C/10(-3) mmHg) carbenically to dibenzo[b,f]pentalene (28, > 48%). 9,10-Anthryldicarbenes 39 or their equivalents convert to pentalene 28 rather than di-peri-cyclobutanthracenes 30 and 31, benzobiphenylene 32, or extended rearrangement products 33-38. Formation of 28 from 24 raises questions with respect to the behavior of 1,3,4,6-cycloheptatetraenyl-1-carbenes 49, 2,4,5,7-cyclooctatetraenylidene 51, 2,5,7-cyclooctatriene-1,4-diylidene 52, 1,2,4,5,7-cyclooctapentaene 53, and bicyclo[4.1.0]heptatrienyl-1-carbenes 54 and to carbon-skeleton and hydrogen rearrangements of anthryldicarbenes 39 and/or their equivalents at various temperatures. 1,5-Bis[methoxy(trimethylsilyl)methyl]anthracenes (25), prepared from 1,5-diiodoanthracene (63) and methoxytrimethylsilylmethylzinc bromide (57, 2 equiv) as catalyzed by PdCl(2)(PPh(3))(2), yield the di-peri-carbenic reaction product 1H,5H-dicyclobuta[de,kl]anthracene (30, > 40%) on pyrolysis at 550-650 degrees C/10(-3) mmHg. Proof of structure and various aspects of the mechanisms of formation of 30 are discussed.     

MEXIT: Maximal un-coupling times for stochastic processes

Classical coupling constructions arrange for copies of the same Markov process started at two different initial states to become equal as soon as possible. In this paper, we consider an alternative coupling framework in which one seeks to arrange for two different Markov (or other stochastic) processes to remain equal for as long as possible, when started in the same state. We refer to this “un-coupling” or “maximal agreement” construction as MEXIT, standing for “maximal exit”. After highlighting the importance of un-coupling arguments in a few key statistical and probabilistic settings, we develop an explicit MEXIT construction for stochastic processes in discrete time with countable state-space. This construction is generalized to random processes on general state-space running in continuous time, and then exemplified by discussion of MEXIT for Brownian motions with two different constant drifts.     

Contours of Brownian processes with several-dimensional times

Summary Two generalisations of Brownian motion to several-dimensional time are considered and the topology of their level sets is analysed. It is shown that for these maps non-trivial contours are quite rare — their union has Lebesgue measure zero. The boundedness of all contours is established for the generalisation due to Lévy. For the other, the Brownian sheet, a partial result concerning the behaviour of the zero contour near the boundary is established.Most of the results in this paper were obtained in the course of an S.R.C studentship at the University of Oxford, and appear in the ensuing D. Phil. thesis. I wish to acknowledge the encouragement of my supervisor John Kingman, and the stimulus of correspondence with J.B. Walsh and R. Pyke.     

A spectral method for nonlinear elliptic equations

Let Ω be an open, simply connected, and bounded region in \(\mathbb {R}^{d}\), d ≥ 2, and assume its boundary ?Ω is smooth and homeomorphic to \(\mathbb {S}^{d-1}\). Consider solving an elliptic partial differential equation L u = f(?, u) over Ω with zero Dirichlet boundary value. The function f is a nonlinear function of the solution u. The problem is converted to an equivalent elliptic problem over the open unit ball \(\mathbb {B}^{d}\) in \(\mathbb {R}^{d}\), say \(\widetilde {L}\widetilde {u} =\widetilde {f}(\cdot ,\widetilde {u})\). Then a spectral Galerkin method is used to create a convergent sequence of multivariate polynomials \(\widetilde {u} _{n}\) of degree ≤ n that is convergent to \(\widetilde {u}\). The transformation from Ω to \(\mathbb {B}^{d}\) requires a special analytical calculation for its implementation. With sufficiently smooth problem parameters, the method is shown to be rapidly convergent. For \(u\in C^{\infty } \left (\overline {\Omega }\right ) \) and assuming ?Ω is a C ^∞ boundary, the convergence of \(\left \Vert \widetilde {u} -\widetilde {u}_{n}\right \Vert _{H^{1}}\) to zero is faster than any power of 1/n. The error analysis uses a reformulation of the boundary value problem as an integral equation, and then it uses tools from nonlinear integral equations to analyze the numerical method. Numerical examples illustrate experimentally an exponential rate of convergence. A generalization to ?Δu + γ u = f(u) with a zero Neumann boundary condition is also presented.     

Competitive travelling salesmen problem: A hyper-heuristic approach

We introduce a novel variant of the travelling salesmen problem and propose a hyper-heuristic methodology in order to solve it. In a competitive travelling salesmen problem (CTSP), m travelling salesmen are to visit n cities and the relationship between the travelling salesmen is non-cooperative. The salesmen will receive a payoff if they are the first one to visit a city and they pay a cost for any distance travelled. The objective of each salesman is to visit as many unvisited cities as possible, with a minimum travelling distance. Due to the competitive element, each salesman needs to consider the tours of other salesman when planning their own tour. Since equilibrium analysis is difficult in the CTSP, a hyper-heuristic methodology is developed. The model assumes that each agent adopts a heuristic (or set of heuristics) to choose their moves (or tour) and each agent knows that the moves/tours of all agents are not necessarily optimal. The hyper-heuristic consists of a number of low-level heuristics, each of which can be used to create a move/tour given the heuristics of the other agents, together with a high-level heuristic that is used to select from the low-level heuristics at each decision point. Several computational examples are given to illustrate the effectiveness of the proposed approach.     

Universiti Malaysia Pahang examination timetabling problem: scheduling invigilators

This paper presents a real-world examination timetabling problem from Universiti Malaysia Pahang (UMP), Malaysia. The problem involves assigning invigilators to examination rooms. This problem has received less attention than the examination timetabling problem from the research community partly because no data sets are available in the literature. In modelling, and solving, this problem we assume that there is already an examination timetable in place (this was the subject of our previous work) and the task is to assign invigilators to that timetable. The contributions of this paper are to formally define the invigilator scheduling problem and to present a constructive algorithm that is able to produce good quality solutions that are superior to the solutions produced when using the university's current software. We also include additional constraints taking into account the comments made by the invigilators, which the current system fails to capture. The model we present, we believe, accurately reflects the real-world problem, capturing various aspects of the problem that have not been presented before in the scientific literature. Moreover, the proposed approach adheres to all hard constraints, which the university's current system fails to do.