Accurate masses of unstable rare-earth isotopes by ISOLTRAP

Direct mass measurements of neutron-deficient rare-earth isotopes in the vicinity of ¹⁴⁶Gd were performed with the Penning trap mass spectrometer ISOLTRAP at ISOLDE/CERN. This paper reports on the measurement of more than 40 isotopes of the elements praseodymium, neodymium, promethium, samarium, europium, dysprosium and holmium, that have been measured with a typical accuracy of m 14 keV. An atomic mass evaluation has been performed taking into account other experimental mass values via a least-squares adjustment. The results of the adjustment are discussed. Received: 18 April 2000 / Accepted: 12 July 2000     

Blow up for a class of quasilinear wave equations in one space dimension

For suitable σ and F, we prove that all classical solutions of the quasilinear wave equation , with initial data of compact support, develop singularities in finite time. The assumptions on σ and F include in particular the model case , for q ⩾ 2,and ϵ = ±1. The starting point of the proof is to write the equation under the form of a first order system of two equations, in which F(ϕ) appears as a nonlocal term. Then, we present a new idea to control the effect of this perturbation term, and we conclude the proof by using well‐known methods developed for 2 × 2 systems of conservation laws. Copyright © 2000 John Wiley & Sons, Ltd.     

A nearly optimal preconditioning based on recursive red–black orderings

Considering matrices obtained by the application of a five-point stencil on a 2D rectangular grid, we analyse a preconditioning method introduced by Axelsson and Eijkhout, and by Brand and Heinemann. In this method, one performs a (modified) incomplete factorization with respect to a so-called ‘repeated’ or ‘recursive’ red–black ordering of the unknowns while fill-in is accepted provided that the red unknowns in a same level remain uncoupled. Considering discrete second order elliptic PDEs with isotropic coefficients, we show that the condition number is bounded by 𝒪(n ${}^{\text{½ log}{}_{\text{2}}\text{(√(5) −1)}}$ ) where n is the total number of unknowns (½ log₂(√(5) − 1) = 0.153), and thus, that the total arithmetic work for the solution is bounded by 𝒪(n^1.077). Our condition number estimate, which turns out to be better than standard 𝒪(log² n) estimates for any realistic problem size, is purely algebraic and holds in the presence of Neumann boundary conditions and/or discontinuities in the PDE coefficients. Numerical tests are reported, displaying the efficiency of the method and the relevance of our analysis. © 1997 John Wiley & Sons, Ltd.     

Nonexistence of small,odd breathers for a class of nonlinear wave equations

In this note, we show that for a large class of nonlinear wave equations with odd nonlinearities, any globally defined odd solution which is small in the energy space decays to 0 in the local energy norm. In particular, this result shows nonexistence of small, odd breathers for some classical nonlinear Klein Gordon equations, such as the sine-Gordon equation and \(\phi ^4\) and \(\phi ^6\) models. It also partially answers a question of Soffer and Weinstein (Invent Math 136(1): 9–74, p 19 1999) about nonexistence of breathers for the cubic NLKG in dimension one.     

Design of a compressed air modulator to be used in comprehensive multidimensional gas chromatography and its application in the determination of pesticide residues in grapes

In this study, a new modulator that is simple, robust and presents low operation costs, was developed. This modulator uses compressed air to cool two small portions in the first centimeters of the second chromatographic column of a comprehensive multidimensional gas chromatography (GC × GC) system. The results show a variation in the peak area less than 3 and 5% to alkanes and pesticides, respectively. The standard deviations for the retention times in the first and second dimension are around 0.05 min and 0.05 s for all the compounds. The system was optimized with n-alkanes. The GC × GC system proposed was applied in the determination of pyrethroid pesticides (bifenthrin, cypermethrin, deltamethrin, fenvalerate, esfenvalerate, cis- and trans-permethrin) in grape samples. Samples were extracted by the mini-Luke modified method and pesticides were quantified by comprehensive multidimensional gas chromatography with micro electron-capture detection (μECD). The values of method limit of quantification (LOQ) were 0.01–0.02 mg kg⁻¹ for all studied pyrethroid and the values of recovery were between 94.3 and 115.2%, with good precision (RSD < 18.4%), demonstrating that the performance of the total method consisting of a modified Luke extraction method and determination by GC × GC-μECD are satisfactory. This study also showed that the system using a modulator with a double jet of compressed air has the potential for application in the analysis of a wider range of pesticide residues in other commodities since it provides low values of LOQ with acceptable accuracy and precision.     

PROMETHEE-MD-2T method for project selection

Project selection is a real problem of multicriteria group decision making (MCGDM) where each decision maker expresses his/her preferences depending on the nature of the alternatives and on his/her own knowledge over them. Thus, information, as much quantitative as qualitative, coexists. The traditional methods of MCGDM developed for project selection usually discriminates in favour of quantitative information at the expense of qualitative information, and this is due to the capability to integrate this first type of information inside their procedure. In this article, two new multicriteria 2-tuple group decision methods called “Preference Ranking Organisation Method for Enrichment Evaluation Multi Decision maker 2-Tuple-I and II” (PROMETHEE-MD-2T-I and II) are presented. They are able to integrate inside their procedure both quantitative and qualitative information in an uncertain context. This has been performed by integrating a 2-tuple linguistic representation model dealing with non-homogeneous and imprecise information data made up by valued intervals, numerical and linguistic values into the aggregation operators of Promethee methods. Although they have been developed for project selection problems, these proposed methods can be applied to all kinds of decision-making problems with heterogeneous and multigranular information.     

Intermittencies on tori: A way to characterize them

Since the three types of intermittency have been theoretically described, many experimental observations of such regimes have been reported. Chaotic behaviors occurring after torus breakdowns and quasi-periodic regimes are also very often observed. It is not so surprising that intermittencies on tori were never reported as soon as it is understood that these common characteristic of intermittencies should be investigated in a Poincaré section of a Poincaré section, that is, in a set which is not possible to define. A specific approach is therefore required to identify them as shown in the paper with two examples of type-I intermittency on tori solution to two different systems.     

Screening approach for chiral separation of pharmaceuticals IV. Polar organic solvent chromatography

The aim of this work is to determine generic screening conditions and an initial simple separation strategy allowing the rapid separation of drug enantiomers in polar organic solvent chromatography (POSC). Four cellulose/amylose-based stationary phases were investigated in detail using two mobile phase basis solvents commonly applied in this mode, i.e. acetonitrile and methanol. Polar mode is interesting for use in purification of enantiomers. In a first step, the parameters potentially influencing the separation, such as addition of an alcohol to the polar organic solvent or the type of mobile phase additive(s), were examined by means of experimental designs. Afterwards, the factors found most important are investigated in more detail. Results showed that the cellulose- and amylose-based stationary phases have very broad and complementary enantiorecognition abilities in the POSC mode. The type of organic solvent for the mobile phase appeared to have a dramatic influence on the quality of the separation. Based on the results, a screening strategy was proposed. Enantioseparation was observed in more than 85% of the tested compounds and analysis times of last eluted peak were usually below 10 min.     

Precision study on capillary electrophoresis methods for metacycline

A CE method for metacycline (MTC) determination was investigated in an inter-laboratory experiment. Many problems were encountered in this study, most of which were related to the transfer of the method to different CE equipment. The reported problems could be classified into different categories: problems related to the precision, to the parameters in the protocol, and to the MTC peak shape. As the peak shape problem was partially responsible for the poor precision, a new CE method was developed in order to obtain a good MTC peak shape on all equipment. The precision of this new method for MTC determination was examined in an intermediate precision study, where the influence of the factors "time" and "equipment" was investigated. Although the new method could be transferred to different instruments, the precision remained poor mainly due to the contributions of the between-replicate and the between-injection variances.