The impact of stochastic lead time reduction on inventory cost under order crossover

We use exponential lead times to demonstrate that reducing mean lead time has a secondary reduction of the variance due to order crossover. The net effect is that of reducing the inventory cost, and if the reduction in inventory cost overrides the investment in lead time reduction, then the lead time reduction strategy would be tenable.We define lead time reduction as the process of decreasing lead time at an increased cost. To date, decreasing lead times has been confined to deterministic instances. We examine the case where lead times are exponential, for when lead times are stochastic, deliveries are subject to order crossover, so that we must consider effective lead times rather than the actual lead times. The result is that the variance of these lead times is less than the variance of the original replenishment lead times.Here we present a two-stage procedure for reducing the mean and variance for exponentially distributed lead times. We assume that the lead time is made of one or several components and is the time between when the need of a replenishment order is determined to the time of receipt.     

Environmentally benign nanomixing by sonication in high-pressure carbon dioxide

Due to the increased use of nanocomposites, mixing at nanoscale has become important. Current mixing techniques can be classified into: (a) dry mixing (mechanical mixing), (b) wet mixing, and (c) simultaneous production of mixed nanoparticles (when possible). Dry mixing is in general not effective in achieving desired mixing at nanoscale, whereas wet mixing suffers from different disadvantages like nanomaterial of interest should be insoluble, has to wet the liquid, and involves additional steps of filtration and drying. This paper examines the use of pressurized carbon dioxide having high density and low viscosity to replace the liquids (e.g., n-hexane, toluene). Ultrasound is applied to the suspension of nanopowders in gaseous and supercritical carbon dioxide where high impact collisions during sonication help mixing and the final mixture is obtained by simple depressurization. The method is tested for binary mixture of alumina/silica, silica/titania, MWNT (multiwalled carbon nanotubes)/silica, and MWNT/titania. The effects of sonication intensity and pressure on the degree of mixing are studied. Comparative study is also done with liquid n-hexane as a mixing media. Quantitative characterization (e.g., mean composition standard deviation, intensity of segregation) of mixing of alumina/silica and silica/titania is done with energy-dispersive X-ray spectroscopy, and that of MWNT/silica and MWNT/titania is done using field-emission scanning electron microscopy and day-light illumination spectrophotometry. Results show that mixing in carbon dioxide at higher ultrasound amplitudes is as good as in liquid n-hexane, and the final mixed product does not contain any residual media as in the case of liquid n-hexane.     

Synthesis of 3-methoxy-quinoxalin-2-ones from methyl trimethoxyacetate and phenylenediamines

Treatment of phenylenediamines with methyl trimethoxyacetate led to the formation of 3-methoxy-quinoxalin-2-ones with the assistance of lanthanide-based Lewis acids.     

General WP-Bailey chains

Motivated by a recent paper of Liu and Ma, we describe a number of general WP-Bailey chains. We show that many of the existing WP-Bailey chains (or branches of the WP-Bailey tree), including chains found by Andrews, Warnaar and Liu and Ma, arise as special cases of these general WP-Bailey chains. We exhibit three new branches of the WP-Bailey tree, branches which also follow as special cases of these general WP-Bailey chains. Finally, we describe a number of new transformation formulae for basic hypergeometric series which arise as consequences of these new WP-Bailey chains.     

Viscoelastic flow in a two-dimensional collapsible channel

We compute the flow of three viscoelastic fluids (Oldroyd-B, FENE-P, and Owens blood model) in a two-dimensional channel partly bounded by a tensioned membrane, a benchmark geometry for fluid–structure interactions. The predicted flow patterns are compared to those of a Newtonian liquid. We find that computations fail beyond a limiting Weissenberg number. Flow fields and membrane shape differ significantly because of the different degree of shear thinning and molecular extensibility underlying the three different microstructural models.     

Pressure effect on heterogeneous trifluoromethylation of fullerenes and its application

The first systematic study of heterogeneous fullerene trifluoromethylation using an innovative gradient-temperature gas-solid reactor revealed a significant effect of CF₃I pressure on the conversion of C₆₀ and C₇₀ into trifluoromethylated products and on the range of fullerene(CF₃)_n compositions that were obtained. The design of the reactor allowed us to lower the residence times of fullerene(CF₃)_n species in the hot zone which resulted in the significant differences in relative isomeric distributions as compared to the earlier methods. For the first time, gram quantities of trifluoromethylated fullerenes were prepared using the new reactor, and the selective synthesis of a single-isomer C₆₀(CF₃)₂ was developed. The relative reactivity of C₇₀ as a CF₃ radical scavenger was found to be much lower than that of C₆₀, especially at an early radical addition stage, which led to the cost-efficient synthesis of C₆₀(CF₃)₂ from a fullerene extract.