Two modifications of the least cost per period heuristic for dynamic lot-sizing

This paper proposes two constructive heuristics for the well-known single-level uncapacitated dynamic lot-sizing problem. The proposed heuristics, called net least period cost (nLPC) and nLPC(i), are developed by modifying the average period cost concept from Silver and Meal's heuristic, commonly known as least period cost (LPC). An improved tie-breaking stopping rule and a locally optimal decision rule are proposed in the second heuristic to enhance performance. We test the effectiveness of the proposed heuristics by using 20 benchmarking test problems frequently used in the literature. Furthermore, we perform a large-scale simulation study involving three factors, 50 experimental conditions, and 100?000 randomly generated problems to evaluate the proposed heuristics against LPC and six other well-known constructive heuristics in the literature. The simulation results show that both nLPC and nLPC(i) produce average holding and setup costs lower than or equal to those of LPC in every one of the 50 experimental conditions. The proposed heuristics also outperform each of the six other heuristics evaluated in all experimental conditions, without an increase in computational requirements. Lastly, considering that both nLPC and nLPC(i) are fairly simple for practitioners to understand and that lot-sizing heuristics have been commonly used in practice, there should be a very good chance for practical applications of the proposed heuristics.     

Highly accurate calculation of radial spheroidal functions

A new method for calculating the radial spheroidal functions of the first kind is proposed for the arguments that are greater than unity in modulus. A well-known representation of these functions is refined and used for this purpose. The constructs and the software implementation proposed in the paper provide an efficient tool for the calculation of the functions with a desired accuracy in a wide range of parameters.     

INFLUENCE OF A LEVELNESS DEFECT IN A THRUST BEARING ON THE DYNAMIC BEHAVIOUR OF AN ELASTIC SHAFT

This paper examines the non-linear dynamic behaviour of a flexible shaft. The shaft is mounted on two journal bearings and the axial load is supported by a defective hydrodynamic thrust bearing at one end. The defect is a levelness defect of the rotor. The thrust bearing behaviour must be considered to be non-linear because of the effects of the defect. The shaft is modelled with typical beam finite elements including effects such as the gyroscopic effects. A modal technique is used to reduce the number of degrees of freedom. Results show that the thrust bearing defects introduce supplementary critical speeds. The linear approach is unable to show the supplementary critical speeds which are obtained only by using non-linear analysis.     

Effect of hydrogen on the photoelectronic properties of GaAs/InGaAs quantum-well heterostructures with an island palladium layer on the surface

The effect of hydrogen on the photoluminescence and planar conductivity of GaAs/InGaAs quantum-well heterostructures with an island Pd layer at the anodically oxidized surface was studied. Unlike continuous deposited Pd layers, island layers do not cause the formation of defects in the GaAs surface region and yet the Pd layer maintains high catalytic activity with respect to hydrogen. It is found that the thermal treatment of such a structure in a hydrogen atmosphere causes atomic-hydrogen passivation of the defects in quantum wells. Studies of the characteristics of planar photoresistors with an island Pd layer acting as hydrogen sensors show that their hydrogen detectivity is approximately two orders of magnitude higher than that of diode structures with continuous Pd layers.     

High-throughput screening of fuel cell electrocatalysts

The drawbacks of our earlier report of preparing fuel cell catalyst arrays by borohydride reduction of inkjet prepared arrays of metal salts are discussed along with the need for inclusion of state-of-the-art metrics in all array screening. An alternative method for screening of hydrogen/air cathode catalysts, direct methanol fuel cell (DMFC) anode catalysts, and catalyst loading studies is provided. State-of-the-art Johnson Matthey catalysts were used in control experiments to demonstrate the utility of the array fuel cell for high throughput screening of fuel cell catalysts in the 3-4 mg/cm² range. This report lays out hard learned rules for high throughput screening and demonstrates that the array fuel cell can be used for very precise screening of libraries of membrane electrode assembly (MEA) components without the pitfalls discussed in the introduction.     

Estimates for the Second Order Derivatives of Eigenvectors in Thin Anisotropic Plates with Variable Thickness

For the second order derivatives of eigenvectors in a thin anisotropic heterogeneous plate Ω_h, we derive estimates of their weighted L₂-norms with majorants whose dependence on the plate thickness h and on the eigenvalue number is expressed explicitly. These estimates maintain the asymptotic sharpness throughout the entire spectrum, whereas inside its low-frequency band the majorants remain bounded as h → +0. The latter is a rather unexpected fact, because for the first eigenfunction u¹ of a similar boundary-value problem for a scalar second order differential operator with variable coefficients, the norm ‖∇ _x ² u⁰; L₂(Ω_h)‖ is of order h⁻¹ and grows as h tends to zero. Bibliography: 35 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 308, 2004, pp. 161–180.     

Relativistic shift of the linear Zeeman effect

The efficiency with which a magnetic field acts on sublevels of the first and second doublets of a hydrogen-like atom is shown to vary because of relativistic effects by a factor of 1 ? 2γ(l + 1)/(2l + 3) and 1 ? 2γl/(2l ? 1), respectively, where γ is the ratio of the electron binding energy to the rest energy and l is the quantum number of the orbital angular momentum.