A two-echelon inventory model with lost sales

This paper considers a single-item, two-echelon, continuous-review inventory model. A number of retailers have their stock replenished from a central warehouse. The warehouse in turn replenishes stock from an external supplier. The demand processes on the retailers are independent Poisson. Demand not met at a retailer is lost. The order quantity from each retailer on the warehouse and from the warehouse on the supplier takes the same fixed value Q, an exogenous variable determined by packaging and handling constraints. Retailer i follows a (Q, R_i) control policy. The warehouse operates an (SQ, (S − 1)Q) policy, with non-negative integer S. If the warehouse is in stock then the lead time for retailer i is the fixed transportation time L_i from the warehouse to that retailer. Otherwise retailer orders are met, after a delay, on a first-come first-served basis. The lead time on a warehouse order is fixed. Two further assumptions are made: that each retailer may only have one order outstanding at any time and that the transportation time from the warehouse to a retailer is not less than the warehouse lead time. The performance measures of interest are the average total stock in the system and the fraction of demand met in the retailers. Procedures for determining these performance measures and optimising the behaviour of the system are developed.     

Few-valence-particle excitations around doubly magic 132Sn

Prompt γ-ray cascades in neutron-rich nuclei around doubly-magic ¹³²Sn have been studied using a ²⁴⁸Cm fission source. Yrast states located in the N = 82 isotones ¹³⁴Te and ¹³⁵I are interpreted as valence proton and neutron particle-hole core excitations with the help of shell model calculations employing empirical nucleon-nucleon interactions from both ¹³²Sn and ²⁰⁸Pb regions.     

Amidrazones. 14. The formation of 1,1-disubstituted hydrazines from the base-promoted hydrolysis of 1,l-disubstituted-3-amino-4,5-dihydro-1H-pyrazolium halides: Mechanistic considerations

Three mechanistic pathways are considered for the hydroxide-promoted conversion of 1,1-disubstituted-3-amino-4,5-dihydro-1H-pyrazolium halides 1 to 1,1-disubstituted hydrazines, ammonia and sodium 3-hydroxypropanoate. Evidence presented in this paper supports a hydrolysis mechanism c that is initiated by hydroxide ion addition to the 3-position of 1 to form a tetrahedral intermediate 7 .     

A synthesis of crambescidin 359

A potentially biomimetic synthesis of the guanidine-containing marine natural product crambescidin 359 via a double Michael addition of guanidine to a suitably functionalised bis-enone is reported.     

Multinucleon phenomena and proton spectra characterizing antiproton annihilation at rest in nuclei

Spectra of protons with momenta greater than 500 MeV/c following antiproton annihilation at rest in carbon and uranium nuclei have been measured. They are compared to recent results from other experiments and to predictions of an intranuclear cascade model. Evidence is presented for a substantialB>0 component in the annihilation process, and an estimate of the magnitude of that component is made.     

Determination of 25 elements in the complex oxide mineral zirconolite by analytical electron microscopy

In this paper we describe a technique for the determination of 25 elements in natural zirconolite using energy-dispersive analytical electron microscopy (AEM). The method presented here allows one to quantitatively investigate the chemistry of submicron-scale zones in complex oxide minerals. The effects of electron channeling, thickness variability and variations in detector resolution were minimized by using a controlled set of operating procedures and instrument parameters. To provide a high level of accurayy, k_ATI-factors were determined from standards for most of the 25 elements of interest, including all of the major elements. Each analytical spectrum is reduced to a set of raw peak counts (and errors) using a digital top-hat filter to suppress background followed by multiple least squares fitting of reference spectra. Counting times of 12–15 min per analysis were required to provide suitable counting statistics. Results are presented for zirconolite samples from the contact metamorphic aureole of the Bergell granodiorite intrusion, Switzerland-Italy. A comparison of 43 AEM analyses with 15 analyses obtained by wavelength-dispersive electron probe microanalysis (EPMA) shows that there is excellent agreement between the two data sets in the amounts of individual elements present, chemical trends and overall stoichiometry. An assessment of the combined data set shows that the major substitution mechanisms in the Bergell samples are coupled substitutions involving the M5,6- and M8-sites of the zirconolite structure: ^M8Ca²⁺ + ^M5,6Ti⁴⁺→^M8REE³⁺ + ^M5,6(Al,Fe)³⁺ and ^M8Ca²⁺ + ^M5,6Ti⁴⁺→^M8(Th,U)⁴⁺ + ^M5,6 (Mg,Fe)²⁺.