A two-echelon base-stock inventory model with Poisson demand and the sequential processing of orders at the upper echelon

We consider a two-echelon inventory system with a number of non-identical, independent ‘retailers’ at the lower echelon and a single ‘supplier’ at the upper echelon. Each retailer experiences Poisson demand and operates a base stock policy with backorders. The supplier manufactures to order and holds no stock. Orders are produced, in first-come first-served sequence, with a fixed production time. The supplier therefore functions as an M/D/1 queue. We are interested in the performance characteristics (average inventory, average backorder level) at each retailer. By finding the distribution of order lead time and hence the distribution of demand during order lead time, we find the steady state inventory and backorder levels based on the assumption that order lead times are independent of demand during order lead time at a retailer. We also propose two alternative approximation procedures based on assumed forms for the order lead time distribution. Finally we provide a derivation of the steady state inventory and backorder levels which will be exact as long as there is no transportation time on orders between the supplier and retailers. A numerical comparison is made between the exact and approximate measures. We conclude by recommending an approach which is intuitive and computationally straightforward.     

Nitroxide‐mediated radical polymerization of 2‐(dimethylamino)ethyl acrylate and its sequential block copolymerization with styrene and N‐butyl acrylate

Nitroxide‐mediated radical polymerization (NMRP) of 2‐(dimethylamino)ethyl acrylate (DMAEA) was carried out at 100–120 °C, initiated by MONAMS, an alkoxyamine based on N‐tert‐butyl‐N‐(1‐diethyl phosphono‐2,2‐dimethylpropyl)nitroxide, SG1. Controlled polymerization can be achieved by the addition of free SG1 (the initial molar ratio of SG1 to MONAMS ranged from 0.06 to 0.12), giving a linear first‐order kinetic plot up to 55–70% conversion depending on the reaction conditions. The molecular weights show a near linear increase with conversion; however, they deviate to some extent with theoretical values. SG1‐mediated polymerization of DMAEA at 112 °C is also controlled in organic solvents (N,N‐dimethylformide, anisole, xylene). Polymerization rate increases with increasing solvent polarity. Chain transfer to polymer produces ～1 mol % branches in bulk and 1.2–1.9 mol % in organic solvents, typical of those for acrylates. From poly(styrene) (pS) and poly(n‐butyl acrylate) (pBA) macroinitiators, amphiphilic di‐ and triblock copolymers p(S‐b‐DMAEA), p(DMAEA‐b‐S‐b‐DMAEA), p(BA‐b‐DMAEA), and p(DMAEA‐b‐BA‐b‐DMAEA) were synthesized via NMRP at 110 °C. Polymers were characterized by GPC, NMR, surface tension measurements, and DSC. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 414–426, 2006     

Synthesis of poly(ethylene oxide) with pending 2,2,6,6‐tetramethylpiperidine‐1‐oxyl groups and its further initiation of the grafting polymerization of styrene

A new stratagem for the synthesis of amphiphilic graft copolymers of hydrophilic poly(ethylene oxide) as the main chain and hydrophobic polystyrene as the side chains is suggested. A poly(ethylene oxide) with pending 2,2,6,6‐tetramethylpiperidine‐1‐oxyls [poly(4‐glycidyloxy‐2,2,6,6‐tetramethylpiperidine‐1‐oxyl‐co‐ethylene oxide)] was first prepared by the anionic ring‐opening copolymerization of ethylene oxide and 4‐glycidyloxy‐2,2,6,6‐tetramethylpiperidine‐1‐oxyl, and then the graft copolymerization of styrene was completed with benzoyl peroxide as the initiator in the presence of poly(4‐glycidyloxy‐2,2,6,6‐tetramethylpiperidine‐1‐oxyl‐co‐ethylene oxide). The polymerization of styrene was under control, and comblike, amphiphilic poly(ethylene oxide)‐g‐polystyrene was obtained. The copolymer and its intermediates were characterized with size exclusion chromatography, ¹H NMR, and electron spin resonance in detail. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3836–3842, 2006     

Metallocene copolymers of propene and 1‐hexene: The influence of the comonomer content and thermal history on the structure and mechanical properties

The relationships between the structure and properties have been established for copolymers of propylene and 1‐hexene synthesized with an isotactic metallocene catalyst system. The most important factor affecting the structure and properties of these copolymers is the comonomer content. The thermal treatment, that is, the rate of cooling from the melt, is also important. These factors affect the thermal properties, the degree of crystallinity, and therefore the structural parameters and the viscoelastic behavior. A slow cooling from the melt favors the formation of the γ phase instead of the α modification. Regarding the viscoelastic behavior, the β relaxation, associated with the glass‐transition temperature, is shifted to lower temperatures and its intensity is increased as the 1‐hexene content raises. The microhardness values are correlated with those of the storage modulus deduced from dynamic mechanical thermal analysis curves, and good linear relations have been obtained between these parameters. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1253–1267, 2006     

Nuclear spin-lattice relaxation mechanisms in kaolinite confirmed by magic-angle spinning

Spin-lattice relaxation mechanisms in kaolinite have been reinvestigated by magic-angle spinning (MAS) of the sample. MAS is useful to distinguish between relaxation mechanisms: the direct relaxation rate caused by the dipole-dipole interaction with electron spins is not affected by spinning while the spin diffusion-assisted relaxation rate is. Spin diffusion plays a dominant role in ¹H relaxation. MAS causes only a slight change in the relaxation behavior, because the dipolar coupling between ¹H spins is strong. ²⁹Si relaxes directly through the dipole-dipole interaction with electron spins under spinning conditions higher than 2 kHz. A spin diffusion effect has been clearly observed in the ²⁹Si relaxation of relatively pure samples under static and slow-spinning conditions. ²⁷Al relaxes through three mechanisms: phonon-coupled quadrupole interaction, spin diffusion and dipole-dipole interaction with electron spins. The first mechanism is dominant, while the last is negligibly small. Spin diffusion between ²⁷Al spins is suppressed completely at a spinning rate of 2.5 kHz. We have analyzed the relaxation behavior theoretically and discussed quantitatively. Concentrations of paramagnetic impurities, electron spin-lattice relaxation times and spin diffusion rates have been estimated.     

Fermi and Coulomb correlations in the 21 S state of the helium isoelectronic sequence

The Fermi and Coulomb holes of the 2¹ S state of the helium isoelectronic sequence are investigated. Several interesting differences between the results obtained and those which might be expected on the basis of the corresponding 2³ S state are pointed out and discussed.     

Stationary phase properties of the organic molten salt ethylpyridinium bromide in gas chromatography

Summary The organic molten salt, 1-ethylpyridinium bromide, is suitable for use as a stationary phase in gas chromatography. It has a usable liquid temperature range of 110 to 160°C. It undergoes a single phase transition at 110°C which corresponds to the bulk melting point. Below the melting point the phase may be used as a selective adsorbent, although column efficiency and peak symmetry deteriorate as the temperature is lowered from the melting point. Above the melting point, ethylpyridinium bromide can be used to separate a wide variety of organic compounds retaining strongly those compounds possessing large dipole or hydrogen bonding functional groups.     

锰（Ⅱ）—邻菲口罗啉配合物极谱吸附波及其应用

在ｐＨ９．５ＮＨ３ＮＨ４Ｃｌ缓冲溶液中，Ｍｎ（Ⅱ）与邻菲口罗啉形成的配合物在－１．３６Ｖ（ｖｓ．ＳＣＥ）处产生一灵敏的吸附波，一阶导数峰电流与Ｍｎ（Ⅱ）浓度在５×１０－８５×１０－６ｍｏｌ／Ｌ范围内呈线性关系，检出限为２×１０－８ｍｏｌ／Ｌ对极谱性质及反应机理进行了研究，用该法测定了大豆和茶叶中的微量锰，结果满意     

FFC-1离子交换纤维对酸碱有害气体吸附性能的研究

系统考察了不同直径及反离子形式的FFC-1聚羧酸离子交换纤维对酸碱有害气体的穿透吸附,各种温、湿度条件下的吸水率,以及作为有害气体吸附滤除材料的重复使用与再生性能。研究表明:FFC-1纤维直径的减小有利于提高对有害气体的动态吸附容量。在体系温度、相对湿度分别为15℃、50%时,以3D腈纶为起始原料的钠型FFC-1离子交换纤维的吸水率≥350mg/g.纤维;对SO2的穿透吸附容量可达200mg/g.纤维。FFC-1离子交换纤维具有良好的重复使用与再生能力,经20次再生循环使用后,纤维交换容量未见明显变化。     

Constitution moleculaire d'α,ω-difluoropolydimethylsiloxanes equilibres obtenus par une reaction de redistribution

α,ω-Difluoropolydimethylsiloxanes F[(CH₃)₂SiO]_n(CH₃)₂SiF have been prepared by reaction of (CH₃)₂SiF₂ with cyclic dimethylsiloxanes [(CH₃)₂SiO]_n (n = 3 or 4). An equilibrium is reached in the redistribution of fluorine vs. oxygen atoms after ca. 24 h at 200°C or 15 days at 150°C when catalysed by AlCl₃. 16 equilibrated samples of varied (R = F/Si) overall compositions have been analysed by ¹H and ¹⁹F NMR and by VPC. The presence of rings has been established for the lower values of R. The molecular constitution of the equilibrated samples is described by a set of constants. The abundance of the end units

is slightly larger than expected from random distribution. The good resolution of the spectra permits the distinguishing of the 9th order of environment of the end units and the 5th order for the middle units and the verification that there is no preferential association among the building units, and thus the proportion of chains of various lengths obeys Flory's random distribution mode. The equilibrium molecular constitution of these α,ω-difluorosiloxanes is close to that of their dichloro analogs; the substitution of chlorine by fluorine atoms at the end of the chains thus appears to cause little perturbation. On the other hand, the kinetic evolution of the reaction appears to be different, since the first species which forms is always the pyro molecule

instead of long chains and large rings as in the case of the chloro analogs.