Two-dimensional separations and behaviour of alkaloids of various polarities on unmodified silica gel in polar and very polar neutral or acidic mobile phases

Summary New separation procedures for alkaloids of similar polarity and structure or of very different polarity and structure, based upon two-dimensional thin-layer chromatography on unmodified silica gel under mild conditions are described. Separation factors and separation mechanisms based on the structure of the bases and mobile phase composition are discussed for some examples of very efficient procedures.Proportions in solvent mixtures are v/v except where otherwise indicated.     

The determination of starting conditions for modifier optimization in reversed-phase HPLC

Summary After a brief introduction of the subject, the paper focusses on the first step in any optimization procedure: the delineation of the parameter space, wherein the global optimum is to be found. For organic modifier optimization in reversed-phase liquid chromatography it is shown that the necessary information can be derived from a single water-methanol gradient. It first yields an estimate of the total number of solutes in the sample, which is vital to define the peak capacity needed to achieve separation at a certain confidence level. Next, the gradient allows the prediction of suitable isocratic methanol binary solvents, and transfer rules formulate the iso-eluotropic composition of the common binary solvents (tetrahydrofuran and acetonitrile). Because all predictions are based on a statistical analysis of a limited data base, attention is given to the practical situation where an actual sample deviates from the average solute behaviour. Such deviations are revealed in the first isocratic run and can be used to arrive at a better estimate of solute retention.     

Synthesis of α, ω perfluoropolyether iodides

Perfluoropolyether (PFPE) diacyl halides of formula XCOCF₂O[(CF₂O)_n(CF₂CF₂O)_m]_pCF₂COX, with X = Cl, F and molecular weight (MW) 400-4000 g mol⁻¹ are smoothly converted in high yields to the corresponding α, ω diiodides in the absence of solvent, employing KI or LiI at 210 °C with extrusion of CO. During the reactions, β-elimination of COF₂ from the terminal difluoromethylene oxide units (CF₂O, C₁ unit) occurs to some extent until a tetrafluoroethylene oxide unit (OCF₂CF₂, C₂ unit) is encountered yielding a OCF₂CF₂I terminus. This considerably alters the MW distribution of the final diiodide especially for low MW PFPEs. Operating in supercritical conditions of CO (scCO) or both scCO and CO₂ (scCO₂) on low (<600 g mol⁻¹) MW diacyl halides, lowers β-elimination from 95 to 52 mol% if KI is used or from 43 to 30 mol% if LiI is used. With higher MW (>600 g mol⁻¹) β-elimination is lowered from 15 to <1 mol% in scCO conditions employing KI.     

Convexlike and concavelike conditions in alternative,minimax, and minimization theorems

Convexlike and concavelike conditions are of interest for extensions of the Von Neumann minimax theorem. Since the beginning of the 80's, these conditions also play a certain role in deriving generalized alternative theorems of the Gordan, Motzkin, and Farkas type and Lagrange multiplier results for constrained minimization problems.In this paper, we study various known convexlike conditions for vector-valued functions on a set and investigate convexlike and concavelike conditions for real-valued functions on a product setC×D, where we are mainly interested in the relationships between these conditions. At the end of the paper, we point out several conclusions from our results for the above-mentioned mathematical fields.The author is indebted to Dr. R. Reemtsen and Dr. V. Jeyakumar for their helpful comments during the preparations of this paper.     

原子荧光光谱法测定砷过程中还原反应条件的优化

自然界中砷和砷的化合物一般可通过水、大气和食物等途径进入人体,危害人体健康,原子荧光光谱法测定砷含量被广泛应用。为准确测定样品中砷的含量,以原子荧光光谱法(AFS)测定土壤中总砷含量为例,重点研究高价态砷(Ⅴ)还原为低价态砷(Ⅲ)的实验条件,采用正交实验进行条件优化,建立适合的实验方法。通过设计L9(34)正交实验,高价态砷的还原反应与四个因素有关,即与反应温度、反应时间、盐酸加入量和硫脲的用量呈一定的正相关,结果表明,四个因素中硫脲用量的影响最为显著,其次是盐酸加入量、反应时间和反应温度。通过对四个因素的多水平检验,优化后的实验条件为：硫脲用量2.0 mL、盐酸加入量10%、反应时间20 min、温度20～35 ℃(即普通室温)。采用土壤标准物质验证优化后条件的可行性,得出砷的测定值在标准值范围内,RSD在2.2%～4.2%,精密度和准确性均满足质控要求。优化后的实验条件使得操作简便易行,提高了工作效率。     

Efficient Oxidation of Cyclohexane over Bulk Nickel Oxide under Mild Conditions

Nickel oxide powder was prepared by simple calcination of nickel nitrate hexahydrate at 500 °C for 5 h and used as a catalyst for the oxidation of cyclohexane to produce the cyclohexanone and cyclohexanol—KA oil. Molecular oxygen (O₂), hydrogen peroxide (H₂O₂), t-butyl hydrogen peroxide (TBHP) and meta-chloroperoxybenzoic acid (m-CPBA) were evaluated as oxidizing agents under different conditions. m-CPBA exhibited higher catalytic activity compared to other oxidants. Using 1.5 equivalent of m-CPBA as an oxygen donor agent for 24 h at 70 °C, in acetonitrile as a solvent, NiO powder showed exceptional catalytic activity for the oxidation of cyclohexane to produce KA oil. Compared to different catalytic systems reported in the literature, for the first time, about 85% of cyclohexane was converted to products, with 99% KA oil selectivity, including around 87% and 13% selectivity toward cyclohexanone and cyclohexanol, respectively. The reusability of NiO catalyst was also investigated. During four successive cycles, the conversion of cyclohexane and the selectivity toward cyclohexanone were decreased progressively to 63% and 60%, respectively, while the selectivity toward cyclohexanol was increased gradually to 40%.     

Second-order necessary optimality conditions for domain optimization problems of the Neumann type

In this paper, we treat a domain optimization problem in which the boundary-value problem is a Neumann problem. In the case where the domain is in a three-dimensional Euclidean space, the first-order and the second-order necessary conditions which the optimal domain must satisfy are derived under a constraint which is the generalization of the requisite of constant volume.Portions of this paper were presented at the 13th IFIP Conference on System Modelling and Optimization, Tokyo, Japan, 1987.     

Robust Output Tracking Control of an Uncertain Linear System via a Modified Optimal Linear-Quadratic Method

This study investigates the robust output tracking problem for a class of uncertain linear systems. The uncertainties are assumed to be time invariant and to satisfy the matching conditions. According to the selected nominal parameters, an optimal solution with a prescribed degree of stability is determined. Then, an auxiliary input via the use of an adapting factor, connected to the nominal optimal control, is introduced to guarantee the robustness and prescribed degree of stability for the output tracking control of the uncertain linear systems. This method is very simple and effective and can reject bounded uncertainties imposed on the states. A maglev vehicle model example is given to show its effectiveness.     

New Relaxation Method for Mathematical Programs with Complementarity Constraints

In this paper, we present a new relaxation method for mathematical programs with complementarity constraints. Based on the fact that a variational inequality problem defined on a simplex can be represented by a finite number of inequalities, we use an expansive simplex instead of the nonnegative orthant involved in the complementarity constraints. We then remove some inequalities and obtain a standard nonlinear program. We show that the linear independence constraint qualification or the Mangasarian–Fromovitz constraint qualification holds for the relaxed problem under some mild conditions. We consider also a limiting behavior of the relaxed problem. We prove that any accumulation point of stationary points of the relaxed problems is a weakly stationary point of the original problem and that, if the function involved in the complementarity constraints does not vanish at this point, it is C-stationary. We obtain also some sufficient conditions of B-stationarity for a feasible point of the original problem. In particular, some conditions described by the eigenvalues of the Hessian matrices of the Lagrangian functions of the relaxed problems are new and can be verified easily. Our limited numerical experience indicates that the proposed approach is promising.     

Passive Runge–Kutta Methods—Properties, Parametric Representation, and Order Conditions

In this paper, a new class of Runge–Kutta methods is introduced. Some basic properties of this subgroup of algebraically stable methods are presented and a complete parametric representation is given. Necessary and sufficient order conditions for lower order methods as well as sufficient order conditions for higher order methods are derived yielding a significantly reduced number of conditions when compared with general Runge–Kutta methods. Design examples conclude this paper.