Spatial and temporal variation in the stable isotope composition (δ18O and δ2H) of rain across the tropical island of Sri Lanka

Seasonal and spatial variation in δ¹⁸O and δ²H in rainwater was determined in three selected transects across Sri Lanka, the tropical island in the Indian Ocean. Local meteoric water lines (LMWLs) for three distinguished climatic zones; wet, dry and intermediate were constructed. LMWLs show slight variations in their gradients and respective d-excess values, depending on the air moisture origin, circulation and environmental conditions of each climatic zone. The elevation effect and amount effect could be identified but the continental effect is not significantly seen in the isotope composition of rain in the concerned areas. The results reasonably revealed that the distinct rainfall regimes; two monsoonal rains and two convectional (inter-monsoon) rains have characteristic isotopic signatures. Also the impact of (i) terrestrial and oceanic moisture sources, (ii) depression and cyclonic conditions of the Bay of Bengal, and (iii) topography of the country on the variation of the isotopic composition of rain in Sri Lanka could be satisfactorily identified.     

Fleet routing position-based model for inventory pickup under production shutdown

This paper addresses the problem of collecting inventory of production at various plants having limited storage capacity, violation of which forces plant shutdowns. The production at plants is continuous (with known rates) and a fleet of vehicles need to be scheduled to transport the commodity from plants to a central storage or depot, possibly making multiple pickups at a given plant to avoid shutdown. One operational objective is to achieve the highest possible rate of product retrieval at the depot, relative to the total travel time of the fleet. This problem is a variant (and generalization) of the inventory routing problem. The motivating application for this paper is barge scheduling for oil pickup from off-shore oil-producing platforms with limited holding capacity, where shutdowns are prohibitively expensive. We develop a new model that is fundamentally different from standard node-arc or path formulations in the literature. The proposed model is based on assigning a unique position to each vehicle visit at a node in a chronological sequence of vehicle-nodal visits. This approach leads to substantial flexibility in modeling multiple visits to a node using multiple vehicles, while controlling the number of binary decision variables. Consequently, our position-based model solves larger model instances significantly more efficiently than the node-arc counterpart. Computational experience of the proposed model with the off-shore barge scheduling application is reported.     

Mathematical modelling of binder removal from plastically-formed engineering ceramics

A mathematical model is developed to quantify the degradation of binder used for plastic forming of ceramic components and the mass transport of the degradation products. A fully-implicit finite-difference method is used to obtain numerical solutions of a non-linear differential equation governing the degradation rate, diffusion coefficient and concentration. It is able to predict the critical linear heating rate below which defects due to boiling can be avoided. Examples are given to illustrate the use of the model to investigate the effect of ceramic powder, supporting powder bed and binder properties on the critical heating rate.Dedicated to Professor J. Crank on the occasion of his 80th birthday     

Bounds on stochastic convex allocation problems

We consider a stochastic convex program arising in a certain resource allocation problem. The uncertainty is in the demand for a resource which is to be allocated among several competing activities under convex inventory holding and shortage costs. The problem is cast as a two–period stochastic convex program and we derive tight upper and lower bounds to the problem using marginal distributions of the demands, which may be stochastically dependent. It turns out that these bounds are tighter than the usual bounds in the literature which are based on limited moment information of the underlying random variables. Numerical examples illustrate the bounds.     

Das Wissen um Unterschiede in den kognitiven Strukturen von Schülerinnen und Schülern als Erklärung von Unterrichtsbeiträgen

It is reported about a longitudinal study run at the Institute of Cognitive Mathematics of the University of Osnabrueck, in which pupils’ verbal and text productions from mathematics lessons at a grammar school are analysed by means of cognitive theoretical methods. First of all, a teaching scene from an instruction to probability calculus and further text productions from an introductory lesson about exponential functions are analysed, in which five pupils take part whose cognitive structures have been assessed and classified in individual examinations. The characteristics brought out according to these teaching scenes indicate different ideas and thinking processes of the pupils. The second part shows that the pupils’ behaviour described is not only to be regarded in isolation but it can also be found in longitudinal examinations and can therefore be considered as a stable, typical characteristic. These results lead to consequences for the planning and design of mathematics lessons based on a well-founded theory of cognition.