Variations on the Theorem of Birkhoff – von Neumann and Extensions

 The theorem of Birkhoff – von Neumann concerns bistochastic matrices (i.e., matrices with nonnegative real entries such that all row sums and all column sums are equal to one). We consider here real matrices with entries unrestricted in sign and we extend the notion of permutation matrices (integral bistochastic matrices); some generalizations of the theorem are derived by using elementary properties of graph theory. Received: October 10, 2000 Final version received: April 11, 2002     

Evidence for a new metastable crystalline phase of strontium nitrate

The undercooling of aqueous solutions of strontium nitrate a few mm³ in volume or microsized by dispersion within an emulsion is investigated. The experimental results are consistent with a succession of transformations in undercooled solutions of binaries. Following concentration, the undercoolings are from 14°C to 20°C for macrosamples or from 39°C to 60°C with emulsions. However it is observed that Sr(NO₃)₂ crystallizes into a metastable phase which can be preserved for a long time. The existence of this metastable crystalline phase has been evidenced by Differential Scanning Calorimetry and by an original evaporation method. The phase diagram, including the metastable phase, is presented.     

Synthesis and characterization of substituted garnet and perovskite-based lithium-ion conducting solid electrolytes

Titanium, tantalum-substituted Li₇La₃Zr_2-xA_xO₁₂ (LLZO, A?=?Ta, Ti) garnets, and chromium-substituted La_(2/3)-xLi_3xTi_1-yCr_yO₃ (LLTO) perovskites were prepared by a conventional solid-state reaction and the Pechini processes. The desired crystal phases were obtained by varying the calcination temperature and time, as well as the substitution concentration. All samples indicated decomposition of the precursors when heated above 750 °C and formation of the desired phase after heat treatment at higher temperatures. Neutron diffraction data shows the formation of a predominant cubic phase in the case of Ta-LLZO, and monoclinic phase with minor impurity phases for Cr-LLTO. Ionic conductivity for Ti-LLZO (Li₇La₃Zr_1.4Ti_0.6O₁₂), Ta-LLZO (Li_6.03La₃Zr_1.533Ta_0.46O₁₂), and Cr-LLTO (La_(2/3)-xLi_3xTi_0.9Cr_0.1O₃) at room temperature were found to be 5.21?×?10^?6, 1.01?×?10^?6, and 1.2?×?10^?4 S cm^?1, respectively. The activation energies of the compounds were determined from the Arrhenius plot and were 0.44 eV (Ti_0.6-LLZO), 0.54 eV (Ta_0.5-LLZO), and 0.20 eV (Cr_0.1-LLTO).     

Remarks on the notion of mean free path for a periodic array of spherical obstacles

In this note, we explain in detail how the notion of mean free path is related to the mathematical results obtained in our previous paper.     

Maxima and minima of the displacement components for the Lamb modes

This paper revisits the vanishing of the transverse component of the particle displacement vector in free surfaces of an isotropic homogeneous plate, for both symmetric and antisymmetric Lamb waves. Drawing on well-known analytical expressions from Viktorov's book [(1967) Rayleigh and Lamb Waves: Physical Theory Applications, Chap. II, pp. 67-121], two distinct frequency-thickness product expressions, in cases where this vanishing occurs, are derived: one for the symmetric modes and another for the antisymmetric modes. At these frequency-thickness products, phase and group velocities have appreciable values which are discussed herein. It appears that these velocities depend on the transverse bulk wave velocity only. This is the specific condition of the Lame? modes. Moreover, theoretical and experimental investigations of displacements in the surface of a plate in air have been carried out. The theoretical part shows that the normal and transverse displacements have, respectively, a local maximum and a local minimum in the vicinity of these frequency-thickness products. The experimental part corroborates the presence of the local maximum of the S(0) Lamb mode for various materials.     

Effects of substituted ligands on the mobility of complexed anions

From conductance and viscosities measurements on Pr₄NCl, Et₄NBr, and AgNO₃ in acetonitrile and Et₃NBr in nitrobenzene, the Walden products of the anion at infinite dilution were determined in presence of various concentrations of substituted benzoic acids. From these data it was possible to compute the values of the Walden products of the once complexed anions and to estimate the order of magnitude of the Walden products of twice complexed anions. Stokes' law is not obeyed, and the Walden products are not proportional to the third root of the molar volume of the complexed ions, as a consequence of their lack of sphericity. The assumption that the drag force which acts on the ions is proportional to the volume of the substituents results in a linear expression between the reciprocals of the Walden products and the molar volume of the ligands. The experimental results fit this expression within the limits of the experimental errors, and the slopes of the lines are nearly the same for all the anions and for the two solvents studied here, namely, 2.5×10^–4 ohm-cm^–5 mole-cP^–1.     

A Chemical Study of Burley Tobacco Flavour (Nicotiana tabacum L.). I. Volatile to medium-volatile constituents (b.p. ≦ 84°/0.001 Torr

The fraction b.p. ≦ 84° (0.001 Torr) from Burley tobacco condensate was carefully investigated using fractional distillation and preparative column and gas liquid chromatography aided by GLC/MS coupling. Among the 193 compounds thus separated and characterized by their spectral data, 81 were newly identified tobacco constituents. Most of the compounds isolated in the course of this work display flavouring properties which make them highly suitable for improving the flavour and aroma of tobacco and tobacco smoke.     

Immunoassay for native enzyme quantification in biological samples

In order to detect low levels of enzyme activity, specifically glucose oxidase, in biological samples, an immunoenzymatic assay was developed since currently available methods could not be used because of either their lack of sensitivity or the conditions prevailing in our samples: turbidity of the medium, presence of redox systems other than glucose oxidase, and high concentration of proteins. The principle of the method is to coat a polystyrene surface with a fragment Fc-specific anti-IgG, then with an antibody directed against the looked-for enzyme, which is simultaneously the antigen and the enzyme activity required for immunoenzymatic detection. We applied this concept to biological samples after glucose oxidase administration to mice. This method achieves specificity and sensitivity (20 ng/mL or 1 ng) with samples of biological origin. No marker is needed since the antigen itself possesses an enzyme activity. This method, which requires a small sample volume (50 ΜL, 20 ΜL, if necessary), can be extended easily to the many enzymes currently used as markers. It could also be applied to the native enzymes of medical interest for which antibodies and a colorimetric reaction are available.     

New C2-Chiral Bidentate Ligands Bridging the gap between donor phosphine and acceptor carbonyl ligands

Two new C₂ chiral bidentate phosphorous ligands have been prepared in enantiomerically pure form. The two phosphorous centers bear electron-withdrawing groups ((CF₃)₂CH? O, C₆F₅) and are linked by a trans-cyclopentane-1,2-diol-derived bridge. Photolysis of [Cr(η⁶-C₆H₆)(CO)₃] in the presence of these two new ligands and of two previously reported bidentate phosphites, and fluorophosphinites (L) afforded [Cr(η⁶-C₆H₆)(CO)L] complexes. IR Spectral comparison of the complexes shows the new ligands to be intermediate in their bonding properties between alkyl phosphites and CO.