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Ant colony optimization for the examination scheduling problem

Ant colony optimization is an evolutionary search procedure based on the way that ant colonies cooperate in locating shortest routes to food sources. Early implementations focussed on the travelling salesman and other routing problems but it is now being applied to an increasingly diverse range of combinatorial optimization problems. This paper is concerned with its application to the examination scheduling problem. It builds on an existing implementation for the graph colouring problem to produce clash-free timetables and goes on to consider the introduction of a number of additional practical constraints and objectives. A number of enhancements and modifications to the original algorithm are introduced and evaluated. Results based on real-examination scheduling problems including standard benchmark data (the Carter data set) show that the final implementation is able to compete effectively with the best-known solution approaches to the problem.     

Existence of solutions for a two point boundary value problem

We consider the two point boundary value problemF[y]=y″?f(x,y,y′)=0,a≤x≤b, y(a)=A, y(b)=B. Assuming thatf satisfies certain differential inequalities associated with the existence ofF-subfunctions andF-superfunctions, and thatf also satisfies a suitable growth condition with respect toy′, we prove that the two point boundary value problem has a solutiony with (x, y(x), y′(x)) in a specified region; indeed we show that the problem has a maximal and a minimal solution in this region. Our results unify and generalize earlier results of K. Ako, L. K. Jackson, M. Nagumo, and others.     

Applications of the Air Lift Fermenter

Since the first development of the airlift fermenter by Le Francois in 1955 (1), the applications have increased to cover most areas of fermentation. This configuration has likewise been developed into many different forms, including: (a) Concentric tube airlift (2); (b) external loop airlift (3); (c) jet loop reactor (4); and (d) propeller loop reactor (4). The subject for discussion in this paper will be the concentric tube airlift, as shown in Fig. (1). This consists of a vertical cylindrical vessel incorporating a concentric draught tube into which is injected a flow of air or other gas mixture suitable for oxygenation. The resulting reduction in bulk density in the central riser causes the contents to move upward thus displacing the contents of the surrounding downcomer, which moves downward, thus inducing circulation of the total contents. This has the advantage of generating liquid mixing and gas transfer without the use of mechanical agitators. The number of possible applications for the airlift fermenter has increased with the advent of genetic engineering techniques that result in new strains of unicellular organisms capable of producing many novel products. An almost universal requirement is the maintenance of absolute sterility, and the absence of agitation with associated shaft seals may be of benefit here. A typical property of some novel organisms is the sensitivity to shear stress of either the product (often a large, easily denatured protein) or the cells themselves, in which there may be an absence of a thick protective cell wall. The airlift fermenter should therefore be of use in these applications.     

A new approximation method for scattering by long finite arrays

The scattering of water waves by a long array of evenly spaced,rigid, vertical circular cylinders is analysed under the usualassumptions of linear theory. These assumptions permit the reductionof the problem to that of solving the Helmholtz equation intwo dimensions, with appropriate circular boundaries. Our primarygoal is to show how solutions obtained for semi-infinite arrayscan be combined to provide accurate and numerically efficientsolutions to problems involving long, but finite, arrays. Theparticular diffraction problem considered here has been chosenboth for its theoretical interest and for its applicability.The design of offshore structures supported by cylindrical columnsis commonplace and understanding how the multiple interactionsbetween the waves and the supports affect the field is clearlyimportant. The theoretical interest comes from the fact that,for wavelengths greater than twice the geometric periodicity,the associated infinite array can support Rayleigh–Blochsurface waves that propagate along the array without attenuation.For a long finite array, we expect to see these surface wavestravelling back and forth along the array and interacting withthe ends. For particular sets of parameters, near-trapping haspreviously been observed and we provide a quantitative explanationof this phenomenon based on the excitation and reflection ofsurface waves by the ends of the finite array.