Optimal Discrete Approximations for Continuous Outcomes with Applications in Decision and Risk Analysis

In decision and risk analysis, it is common to use discrete probability distributions to approximate uncertain events with continuous outcomes. This paper discusses how these approximations may be selected. A class of approximations based on a modification to Taguchi's work on tolerance analysis is shown to be optimal under assumptions of independent uncertainties with normally distributed outcomes. The approximation procedure is shown to be robust in many other situations and is extremely easy to use in practice. We also show how the approximation may be integrated into the process of subjective probability estimation by a ‘subject-matter expert’.     

Optimal Inventory Policies with Service-Level Constraints

In a practical situation it is often difficult to determine the value of the shortage costs for use in in ventory-control systems. However, in cost-minimization problems including service-level constraints, shortage costs are implicitly prevailing. With the purpose of exploring these relations, a continuous review (Q, r) stock-control system is considered, where the order points and lot sizes are computed simultaneously. Instead of explicitly expressing the shortage cost in the objective function, it is taken into consideration through a service-level constraint. The shadow price of this constraint can in some sense be interpreted as the shortage cost corresponding to the requested service level. By changing the value of the service level, interesting relations between shortage costs and service levels can be viewed for different sets of other inventory parameters. In order to investigate the sensitivity for probabilistic variations in the input data, two different probability distributions are used to describe the lead-time demand.     

羰基铁催化黄樟油素、丁香酚异构化反应的研究——Ⅰ.异黄樟油素、异丁香酚的合成

本文报道了异黄樟油素、异丁香酚的新合成途径,即在羰基铁光催化下或多核羰基铁加热催化下,使黄樟油素、丁香酚异构化。其转化率几乎是定量的。反应产物经GC,GC/MC分析及UV,IR,NMR,折光率的鉴定,证明合成过程中发生了异构化反应,而且产物以反式异构体为主。     

三硼酸锂晶体的生长形态

用自由生长系统研究了三硼酸锂ＬｉＢ_３Ｏ_５（ＬＢＯ）晶体的实际生长形态。实验表明，它的各晶面簇的重要性的顺序为：｛１１０｝＞｛０１１｝＞｛２０１｝＞｛１１１｝。讨论了ＬＢＯ晶体的生长习性与内部结构之间的关系并应用负离子配位多面体理论模型解释了ＬＢＯ晶体的生长形态。     

Synthesis,crystal structures and electrochemical properties of group 6 metal carbonyl anion complexes

A series of [M(CO)₅I]⁻ and [M₂(CO)₁₀I]⁻ anion complexes have been synthesized by the photochemical reaction of PhCH₂N(CH₃)₃I or FcCH₂N(CH₃)₃I (Fc=ferrocenyl) with M(CO)₆ (M = Cr, Mo or W), and characterized by elemental analyses, i.r., ¹H-n.m.r. and ¹³C-n.m.r. spectra in the case of the molybdenum and tungsten complexes. These complexes exhibit considerably different electrochemical behavior, when investigated by cyclic voltammetry. The crystal structures of [PhCH₂N(CH₃)₃][Cr(CO)₅I] and [FcCH₂N(CH₃)₃][W₂(CO)₁₀I] have been determined by X-ray diffraction, indicating that only weak contacts maybe exist between anions and cations by the I...H bond in the former, and there are no direct interactions between anions and cations in the latter.     

Transition metal complexes with Girard reagent-based ligands

The ligand, salicylaldehyde Girard-T hydrazonium chloride, [H₂SalGT]Cl (1), and two complexes [Cu(HSalGT)X₂]·H₂O (X = Br(2); Cl(3)) were synthesized and their crystal structures were determined by single-crystal X-ray analysis. In the two isostructural complexes, the Cu(II) is located in a square-pyramidal environment, with the chelating ligand and one halogen atom in the basal plane and the second halogen in the apical position. The most apparent structural difference between the 1 and its complexes 2 and 3 is the orientation of the N(CH₃)₃ group: in 1, it is practically coplanar to the rest of the molecule, while in 2 and 3 it is oriented to the side of the axially bonded halogen, which can be explained by the C–H…X intramolecular interactions. The compounds were characterized by elemental analysis, molar conductivity, magnetic susceptibility and electronic absorption spectra.