An improved approximation algorithm for the two-machine flow shop scheduling problem with an interstage transporter

We study the two-machine flow shop problem with an uncapacitated interstage transporter. The jobs have to be split into batches, and upon completion on the first machine, each batch has to be shipped to the second machine by a transporter. The best known heuristic for the problem is a –approximation algorithm that outputs a two-shipment schedule. We design a –approximation algorithm that finds schedules with at most three shipments, and this ratio cannot be improved, unless schedules with more shipments are created. This improvement is achieved due to a thorough analysis of schedules with two and three shipments by means of linear programming. We formulate problems of finding an optimal schedule with two or three shipments as integer linear programs and develop strongly polynomial algorithms that find solutions to their continuous relaxations with a small number of fractional variables

Constructive notice and independent legal advice: a study of lending institution practice

Cases on when lending institutions will be put on inquiry as to circumstances giving rise to presumption of undue influence, and results of research on lending practice of residential mortgage lenders in light of case law. [From Legal Journals Index]

Kinetic studies of water uptake and loss in glass-ionomer cements

The water sorption and desorption behaviour of three commercial glass-ionomer cements used in clinical dentistry have been studied in detail. Cured specimens of each material were found to show slight but variable water uptake in high humidity conditions, but steady loss in desiccating ones. This water loss was found to follow Fick's law for the first 4-5 h. Diffusion coefficients at 22 degrees C were: Chemflex 1.34 x 10(-6) cm(2) s(-1), Fuji IX 5.87 x 10(-7) cm(2) s(-1), Aquacem 3.08 x 10(-6) cm(2) s(-1). At 7 degrees C they were: Chemflex 8.90 x 10(-7) cm(2) s(-1), Fuji IX 5.04 x 10(-7) cm(2) s(-1), Aquacem 2.88 x 10(-6) cm(2) s(-1). Activation energies for water loss were determined from the Arrhenius equation and were found to be Chemflex 161.8 J mol(-1), Fuji IX 101.3 J mol(-1), Aquacem 47.1 J mol(-1). Such low values show that water transport requires less energy in these cements than in resin-modified glass-ionomers. Fick's law plots were found not to pass through the origin. This implies that, in each case, there is a small water loss that does not involve diffusion. This was concluded to be water at the surface of the specimens, and was termed "superficial water". As such, it represents a fraction of the previously identified unbound (loose) water. Superficial water levels were: Chemflex 0.56%, Fuji IX 0.23%, Aquacem 0.87%. Equilibrium mass loss values were shown to be unaffected by temperature, and allowed ratios of bound:unbound water to be determined for all three cements. These showed wide variation, ranging from 1:5.26 for Chemflex to 1:1.25 for Fuji IX.