A compact formulation of an elastoplastic analysis problem

Two important problems in the area of engineering plasticity are limit load analysis and elastoplastic analysis. It is well known that these two problems can be formulated as linear and quadratic programming problems, respectively (Refs. 1–2). In applications, the number of variables in each of these mathematical programming problems tends to be large. Consequently, it is important to have efficient numerical methods for their solution. The purpose of this paper is to present a method which allows the quadratic programming formulation of the elastoplastic analysis to be reformulated as an equivalent quadratic programming problem which has significantly fewer variables than the original formulation. Indeed, in Section 4, we will present details of an example for which the original quadratic programming formulation required 297 variables and for which the equivalent formulation presented here required only two variables. The method is based on a characterization of the entire family of optimal solutions for a linear programming problem.This research was supported by the Natural Science and Engineering Council of Canada under Grant No. A8189 and by a Leave Fellowship from the Social Sciences and Humanities Research Council of Canada. The author takes pleasure in acknowledging many stimulating discussions with Professor D. E. Grierson.     

The deferred standard method–a technique for quantitative analysis in laboratory and process HPLC

Among the methods of quantitation commonly used in chromatography, the internal standard may be considered as the most useful and accurate; however, use of internal standards in liquid chromatography with UV and fluorometric detectors runs into considerable difficulties because the response factors may differ from each other by several orders of magnitude. Under these conditions, the search for an IS with a response factor similar to that of the analyte and adequately resolved from other peaks may prove very tedious. The deferred standard concept, already used in process and laboratory gas chromatography, is proposed as a solution; its definition, details of instrumentation, operation, and results are described in this paper. The material presented demonstrates its ability to solve this specific problem. In addition, use of the deferred standard approach is seen to save time and money.     

Existence results of a m-point boundary value problem at resonance

Let ξ_i∈(0,1), a_i∈(0,∞), i=1,…,m−2, be given constants satisfying ∑^m−2_i=1a_i=1 and 0<ξ₁<ξ₂<?<ξ_m−2<1. We show the existence of solutions for the m-point boundary value problem

x″=f(t,x,x′),t∈(0,1),     

线性空间中向量极值问题的最优性条件

文 [1]建立了线性拓扑空间中向量极值问题的广义 Kuhn- Tucker条件和 L agrange乘子存在定理 .本文将在线性空间中讨论这方面问题 ,首先在线性空间中建立了次似凸向量值映射的择一定理 ,进而得出序线性空间中向量极值问题的最优性条件及其标量化定理 .     

线性空间中集值映射向量优化问题的最优性条件与Lagrangian乘子

本文在广义次似凸性假设下,利用择一性定理,在线性空间中获得了含等式与不等式约式集值向量最优化问题的Kuhn-Tucker型最优性条件及Lagrangian乘子定理。     

Development and validation of a LC‐MS/MS method for the in vitro analysis of 1‐hydroxymidazolam in human liver microsomes: application for determining CYP3A4 inhibition in complex matrix mixtures

Complementary and alternative medicines (CAM) can affect the pharmacokinetics of anticancer drugs by interacting with the metabolizing enzyme cytochrome P450 (CYP) 3A4. To evaluate changes in the activity of CYP3A4 in patients, levels of 1‐hydroxymidazolam in plasma are often determined with liquid chromatography–quadrupole mass spectrometry (LC‐MS/MS). However, validated LC‐MS/MS methods to determine in vitro CYP3A4 inhibition in human liver microsomes are scarce and not optimized for evaluating CYP3A4 inhibition by CAM. The latter is necessary because CAM are often complex mixtures of numerous compounds that can interfere with the selective measurement of 1‐hydroxymidazolam. Therefore, the aim was to validate and optimize an LC‐MS/MS method for the adequate determination of CYP3A4 inhibition by CAM in human liver microsomes. After incubation of human liver microsomes with midazolam, liquid–liquid extraction with tert‐butyl methyl ether was applied and dried samples were reconstituted in 50% methanol. These samples were injected onto a reversed‐phase chromatography consisting of a Zorbax Extend‐C₁₈ column (2.1 × 150 mm, 5.0 µm particle size), connected to a triple quadrupole mass spectrometer with electrospray ionization. The described LC‐MS/MS method was validated over linear range of 1.0–500 nm for 1‐hydroxymidazolam. The results revealed good inter‐assay accuracy (≥85% and ≤115%) and within‐day and between‐day precisions (coefficient of variation ≤ 4.43%). Furthermore, the applicability of this assay for the determination of CYP3A4 inhibition in complex matrix mixtures was successfully demonstrated in an in vitro experiment in which CYP3A4 inhibition by known CAM (β‐carotene, green tea, milk thistle and St. John's wort) was determined. Copyright © 2013 John Wiley & Sons, Ltd.