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.     

Beyond Flory-Huggins theory: new classes of blend miscibility associated with monomer structural asymmetry

Flory-Huggins (FH) theory is restricted to polymer mixtures whose monomers are structurally identical, a situation limited to isotopic blends and computer simulations. We investigate the influence of monomer structure on blend miscibility and scattering properties using the lattice cluster theory generalization of the FH model. Monomer structural asymmetry is shown to profoundly affect blend miscibility (T(c),phi(c)), chain swelling (T(theta)), and the scale (xi) and intensity [S(0)] of composition fluctuations. Four distinct blend miscibility classes are identified and experimental evidence for these classes is discussed.     

Nowhere monotone functions and functions of nonmonotonic type

We investigate the relationships between the notions of a continuous function being monotone on no interval, monotone at no point, of monotonic type on no interval, and of monotonic type at no point. In particular, we characterize the set of all points at which a function that has one of the weaker properties fails to have one of the stronger properties. A theorem of Garg about level sets of continuous, nowhere monotone functions is strengthened by placing control on the location in the domain where the level sets are large. It is shown that every continuous function that is of monotonic type on no interval has large intersection with every function in some second category set in each of the spaces , and .

     

Approaches to the regiospecific synthesis of Anthracycline antibiotics

Synthetic approaches to anthracycline antibiotics were studied through the use of Claisen rearrangements on 1-methallyloxy-5-methoxyantraquinone (9) which required reducing conditions to proceed through a hydroquinone intermediate in situ. 1-(2′-Methylene-4′-pentenoxy)-5-methoxyanthraquinone (13) underwent a similar reductive rearrangement but also produced a spiro compound 16 as a result of an ene reaction between the phenol and side chain double bond. 1-Hydroxy-2-methally-5-methoxyanthraquinone (11) could not be oxidized to quinizarin 17. 1-Hydroxy-2-methally-5,9,10-trimethoxyanthracene (21) was oxidatively coupled to the dimer at C-2. Dimer 23 reacted with diazomethane to form a 1,3-dipolar adduct 24.     

The application of centre manifolds to amplitude expansions. I. Ordinary differential equations

The theory of centre manifolds for a system of ordinary differential equations is summarized and its relationship to amplitude expansions based upon multiple time scales is discussed. Emphasis is placed upon the practical computational aspects of applying centre manifold theory to near-critical problems, and, in particular, to the computation of the centre manifold. The calculations are illustrated by a detailed analysis of two problems in fluid mechanics.     

Spectroscopic characterization of the matrix–silane coupling agent interface in fiber-reinforced composites

The copolymerizations of anhydride-cured epoxy resin on fiberglass surfaces treated with a N-methylaminopropyltrimethoxysilane coupling agent has been investigated using Fourier-transform infrared spectroscopy. The structure of the interface of the silane and the resin in fiber-reinforced composites is composed of copolymers of the epoxy resin with the organofunctionality of the deposited silanes. The number of interfacial bonds formed depends on the amount of silane coupling agent deposited on the fiberglass and the reaction conditions. The silane induces additional esterification and increases the curing density of the epoxy matrix near the fiber surface by about 5–10% relative to the bulk resin.