Setting local rank constraints by orthogonal projections for image resolution analysis: Application to the determination of a low dose pharmaceutical compound

Raman chemical imaging provides chemical and spatial information about pharmaceutical drug product. By using resolution methods on acquired spectra, the objective is to calculate pure spectra and distribution maps of image compounds. With multivariate curve resolution-alternating least squares, constraints are used to improve the performance of the resolution and to decrease the ambiguity linked to the final solution. Non negativity and spatial local rank constraints have been identified as the most powerful constraints to be used.     

Spectral properties of a tight binding Hamiltonian with period doubling potential

We study a one dimensional tight binding hamiltonian with a potential given by the period doubling sequence. We prove that its spectrum is purely singular continuous and supported on a Cantor set of zero Lebesgue measure, for all nonzero values of the potential strength. Moreover, we obtain the exact labelling of all spectral gaps and compute their widths asymptotically for small potential strength.     

Propriétés statistiques des entiers friables

Let Ψ(x,y) (resp. Ψ_m(x,y)) denote the number of integers not exceeding x that are y-friable, i.e. have no prime factor exceeding y (resp. and are coprime to m). Evaluating the ratio Ψ_m(x/d,y)/Ψ(x,y) for 1≤slantd≤slantx, m≥slant 1, x≥slant y≥slant 2, turns out to be a crucial step for estimating arithmetic sums over friable integers. Here, it is crucial to obtain formulae with a very wide range of validity. In this paper, several uniform estimates are provided for the aforementioned ratio, which supersede all previously known results. Applications are given to averages of various arithmetic functions over friable integers which in turn improve corresponding results from the literature. The technique employed rests mainly on the saddle-point method, which is an efficient and specific tool for the required design.2000 Mathematics Subject Classification: Primary—11N25; Secondary—11K65, 11N37     

Séries trigonométriques à coefficients arithmétiques

Journal d'Analyse Mathématique -     

Collisional parameters of H2O lines: effects of vibration

A complex semiclassical model for the calculation of line widths and shifts of H₂O broadened by N₂, derived from the Robert and Bonamy approach, is tested by comparisons with measurements for selected transitions in various vibrational bands. The lines retained, which involve rotational states with Kc=J or J−1 have been chosen for two reasons. The first is that they show large variations of the widths with J and thus enable a severe test of the model. The second is that, as explained in this paper, they are well-suited for the study of the effects of vibration on the collisional parameters. The measured values have been extracted from an updated version of a database built years ago (JQSRT 52 (1994) 481) that contains all available measurements. Comparisons between experimental and calculated widths and shifts at room temperature illustrate the quality of the model and clearly demonstrate, for the first time, that there is a vibrational dependence of the broadening. Values of collisional parameters are first studied in fundamental bands. This shows that the theoretical approach accounts for most of the dependence of broadening and shifting on rotational quantum numbers: the variations of γ, which reach a factor of nearly 20 from low to high J values, are correctly accounted for by the model as are some specific features of the shifts δ. Analysis confirms that the bending and stretching vibrations have significantly different effects on δ, due to the vibrational dependence of the intermolecular potential. On the other hand, differences on the widths are rather small with slightly smaller broadening for lines of the bending band. Calculations show that there is a spectroscopic effect, due to the larger rotational constant A in the v₂=1 state. Calculations made for overtone bands involving numerous quanta of the stretching vibration are then presented. They predict that a significant dependence of the width should be observed for high J lines due to the effect of vibration on the interaction potential. This is confirmed by comparisons with measurements for lines involving a change of three and four quanta of stretching vibration.     

HAC estimation and strong linearity testing in weak ARMA models

In the framework of ARMA models, we consider testing the reliability of the standard asymptotic covariance matrix (ACM) of the least-squares estimator. The standard formula for this ACM is derived under the assumption that the errors are independent and identically distributed, and is in general invalid when the errors are only uncorrelated. The test statistic is based on the difference between a conventional estimator of the ACM of the least-squares estimator of the ARMA coefficients and its robust HAC-type version. The asymptotic distribution of the HAC estimator is established under the null hypothesis of independence, and under a large class of alternatives. The asymptotic distribution of the proposed statistic is shown to be a standard χ² under the null, and a noncentral χ² under the alternatives. The choice of the HAC estimator is discussed through asymptotic power comparisons. The finite sample properties of the test are analyzed via Monte Carlo simulation.     

A short and highly stereoselective synthesis of α-(2-aminothiazolyl)-C-nucleosides

A short route to novel α-(2-aminothiazolyl)-C-nucleosides has been developed. The key step was the high diastereoselective reduction of the hemiacetal intermediates using L-Selectride, which afforded the corresponding R-diols in quantitative yields. These diols were converted, after C4-C1 ring closure and protecting groups cleavage, to their corresponding free α-C-nucleosides.     

Stationary axisymmetric solutions in the vacuum Jordan-Brans-Dicke theory

It is shown that any stationary axisymmetric solution to the vacuum field equations of the Jordan-Brans-Dicke (JBD) theory may be obtained from a composition of any stationary axisymmetric vacuum Einstein spacetime with the Weyl class of metrics. Thus, generating solution techniques can be used to obtain any stationary axisymmetric JBD vacuum solution. In this manner, C. B. G. McIntosh's results concerning this topic are improved upon.