Analysis of the REDOR Signal and Inversion

An inversion of the REDOR signal to recover the dipolar couplings has been recently proposed [K. T. Muelleret al., Chem. Phys. Lett.242, 535 (1995)]: The corresponding integral transform was performed by tabulation of the kernel followed by numerical integration. After explicit determination of the inverse REDOR kernel by the Mellin transform method, we propose an alternative inversion method based on Fourier transforms. Representation of the inverse REDOR kernel by its asymptotic expansion reveals that the inverse REDOR operator is essentially a weighted sum of a cosine transform and of its derivative. Consequently, known properties of Fourier transforms can easily be transposed to the REDOR inversion, allowing for a precise discussion of the value of the method. Moreover, the first term of the asymptotic expansion leading to a derivative of a cosine transform, the REDOR inversion is found to be extremely sensitive to noise, thus considerably reducing the useful part of the theoretical dipolar window.     

Goussarov-Habiro theory for string links and the Milnor-Johnson correspondence

We study the Goussarov-Habiro finite type invariants theory for framed string links in homology balls. Their degree 1 invariants are computed: they are given by Milnor's triple linking numbers, the mod 2 reduction of the Sato-Levine invariant, Arf and Rochlin's μ invariant. These invariants are seen to be naturally related to invariants of homology cylinders through the Milnor-Johnson correspondence: in particular, an analogue of the Birman-Craggs homomorphism for string links is computed. The relation with Vassiliev theory is studied.     

A First Order Sufficient Condition for Optimality in Nonsmooth Optimization

We derive a simple sufficient condition for a point a∈S?X be a local minimum of f: X → R on S. This condition is of the first order in its nature and takes into account the derivative (or some generalization of it) in a neighborhood of a. Applications like a sufficient condition for (a, b)∈ S × T ? X × Y be a saddle-point of a bivariate function f: X × Y ? R are also proposed.     

Pupils learning algebra with DERIVE

This article deals with the use of computer algebra systems in mathematics secondary education. First, we present the global framework of a research project carried out in France with pupils of grades 9 to 12, from 1993 through 1995. Then we focus on a specific part of this project concerning two grade 9 classes of different mathematical ability taught by the same teacher. We briefly present the aims and organisation of DERIVE's use in the two classes, before embarking with more details on a specific topic: systems of linear equations. Finally, we present the data provided by the pupils' answers to a questionnaire taken at the end of the academic year; we use them for investigating pupils' assumptions about DERIVE's potential for mathematics learning, and compare these representations with those emerging from the entire population.     

Dynamics of a bilayer membrane with membrane-solvent partial slip boundary conditions

We discuss the dynamics of a bilayer membrane with partial slip boundary conditions between the monolayers and the bulk fluid. Using Onsager’s variational principle to account for the associated dissipations, we derive the coupled dynamic equations for the membrane height and the excess lipid density. The newly introduced friction coe?cients appear in the renormalized fluid viscosities. For ordinary lipid bilayer membranes, we find that it is generally justified to ignore the e?ects of permeation and parallel slip at the membrane surface.     

Optimisation of pressurised liquid extraction by experimental design for quantification of pesticides and alkyl phenols in sludge,suspended materials and atmospheric fallout by liquid chromatography–tandem mass spectrometry

The study proposes an analytical method to quantify 10 alkylphenols and 12 pesticides at ultra-trace levels by liquid chromatography in reverse mode coupled to positive electrospray ionisation–tandem mass spectrometry. The extraction procedure from environmental solids was optimised by pressurised liquid extraction using acetonitrile:isopropanol (1:1, v/v). The influence of several extraction experimental factors, temperature, pressure, duration and number of cycles, related to the PLE was investigated by an original and efficient chemometric approach. The optimised extraction method (80 °C, 40 bar, 10 min, 1 cycle) exhibited recoveries between 67 and 127% with RSD mostly under 13%. The whole method was applied to real samples: sludge, suspended materials, atmospheric fallouts and roof deposit. Pollutant levels were between 1 μg kg⁻¹ and 5.9 mg kg⁻¹.     

Comparison of Differing Formulations of the PCM Model by their Application to the Simulation of an Auto-igniting H 2/air Jet

Different combustion models such as PCM (Presumed Conditional Moments) or ADF-PCM (Approximated Diffusion Flames Presumed Conditional Moments) can be used for RANS simulations of non premixed or partially premixed turbulent flames. In this paper, the auto-ignition experiment performed by Mastorakos and co-workers at Cambridge University is used as a validation case for comparing these two approaches. Furthermore, the first order PCM model is introduced to analyze the effects of the progress variable segregation and an improved version of ADF-PCM is developed with a pdf of the scalar dissipation rate. Compared to ADF-PCM models, the first and second order PCM models predict very sharp temperature and progress variable increase after ignition for all simulated cases. The segregation factors of the progress variable reach important values during the ignition for ADF-PCM models whereas for PCM, high values are reached at the beginning of the ignition.     

A 2-basic set of the alternating group

In this note, we construct a 2-basic set of the alternating group \mathfrakA_n{\mathfrak{A}_n}. To do this, we construct a 2-basic set of the symmetric group \mathfrakS_n{\mathfrak{S}_n} with an additional property, such that its restriction to \mathfrakA_n{\mathfrak{A}_n} is a 2-basic set. We adapt here a method developed by Brunat and Gramain (J. Reine Angew. Math., to appear) for the case when the characteristic is odd. One of the main tools is the generalized perfect isometries defined by Külshammer et al. (Invent. Math. 151, 513–552, (2003)).