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.     

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.     

Zur Kenntnis der Burton'schen Regel bei positiven Hydrosolen

Ohne Zusammenfassung     

Ground-state dynamics of α-methylstyrene. I. Thermally induced oligomerization in bulk

α-Methylstyrene (α-Me-St) in bulk undergoes a variety of thermally induced processes which we investigated in detail by product-distribution analysis. The oligomeric products, shown by GC–MS coupling techniques and independent syntheses, consisted of nine dimers and nine trimers with no detectable higher oligomers or polymers. Two isomeric cyclobutanes and one of the open-chain unsaturated dimers were formed by a conventional two-step cycloaddition; a Flory-type diradical was the common intermediate. In contrast to these 2π + 2π products, the majority of the remaining oligomers could not be interpreted on the basis of π-electron interaction between closed shell molecules. Their structures, however, were compatible with a free radical process in which cumyl(MH·) and 1,4-dimethyl-1-phenyl-tetrahydronaphthalene-yl(THN·), which are consecutive products of 4π + 2π and 2π + 2π interactions, respectively, were involved in addition and transfer reactions. Because of the small rate of initiation and the obvious lack of free radical recombination products, a mechanism was suggested in which MH· and THN· radicals react predominantly in a closed sequence of elementary processes and to a rather small extent only by bimolecular free radical termination. Two sorts of stabilization steps, hydrogen transfer to monomer (R_nH· + M → R_n + MH·) and hydrogen abstraction from a hypothetical 4π + 2π intermediate I (R_nH· + I → R_nH₂ + THN·), are attributed to the high rates of unsaturated and saturated oligomer formation.     

Synthesis,coordination to Rh(I), and hydroformylation catalysis of new beta-aminophosphines bearing a dangling nitrogen group: an unusual inversion of a Rh-coordinated P center

Variants of the beta-aminophosphine L(1) [Ph(2)PCH(2)CH(Ph)NHPh] containing additional nitrogen donor functions have been prepared. These functions are branched off the C atom adjacent to the P atom, or the P atom itself. Ligand [Ph(2)PCH(o-C(6)H(4)NMe(2))CH(Ph)NHPh] has been obtained as a mixture of two diastereomers L(3A) and L(3B) by lithiation of L(2) [Ph(2)PCH(2)(o-C(6)H(4)NMe(2))] with n-BuLi followed by PhCH=NPh addition and hydrolysis. The diastereomers have been separated by fractional crystallization from ethanol. Ligand Et(2)NCH(2)P(Ph)CH(2)CH(Ph)NHPh has been obtained as a mixture of two diastereomers L(5A) and L(5B)(starting with P-Ph reductive cleavage of L(1) by lithium and subsequent hydrolysis to give PhP(H)CH(2)CH(Ph)NHPh (mixture of two diastereomers L(4A) and L(4B)). The latter reacts with diethylamine and formaldehyde to afford the L(5) diastereomeric mixture. Complexes RhCl(CO)(L) (L = L(3A), 1(A); L(3B), 1(B); L(5A/B), 2(A/B)) were obtained by reaction of [RhCl(CO)(2)](2) and the appropriate ligand or ligand mixture. Complexes 1(A), 1(B), and 2(A) have been isolated in pure form and characterized by classical techniques and by single-crystal X-ray diffraction. All structures exhibit a bidentate kappa-P,kappa-N(NHPh) mode similar to the complex containing L(1). While complexes 1(A) or 1(B) are stable in CDCl(3) solution, complex 2(A) slowly converts to its diastereomer 2(B). This unexpected epimerization appears to take place by inversion at the Rh-coordinated P center, an apparently unprecedented phenomenon. A mechanism based on a reversible P-C bond oxidative addition is proposed. The influence of the pendant nitrogen function of the diaminophosphines L(3A) and L(5A/B) on the rhodium catalytic activity in styrene hydroformylation has been examined and compared to that of the aminophosphines L(1) or L(2). The observed trends are related to the basicity of the dangling amine function and to its proximity to the metal center.