When random proportional subspaces are also random quotients

We discuss when a generic subspace of some fixed proportional dimension of a finite-dimensional normed space can be isomorphic to a generic quotient of some proportional dimension of another space. We show (in Theorem 4.1) that if this happens (for some natural random structures) then for any proportion arbitrarily close to 1, the first space has a lot of Euclidean subspaces and the second space has a lot of Euclidean quotients.     

An attempt on the calculation of relativistic potential energy curves: Noble gas difluorides

Total energy SCF calculations were performed for noble gas difluorides in a relativistic procedure and compared with analogous non-relativistic calculations. The discrete variational method with numerical basis functions was used. Rather smooth potential energy curves could be obtained. The theoretical Kr-F and Xe-F bond distances were calculated to be 3.5 a.u. and 3.6 a.u. which should be compared with the experimental values of 3.54 a.u. and 3.7 a.u. Although the dissociation energies are off by a factor of about five it was found that ArF₂ may be a stable molecule. Theoretical ionization energies for the outer levels reproduce the experimental values for KrF₂ and XeF₂ to within 2 eV.     

Conjecture de Franchetta forte

Sans résumé     

The Module Structure Theorem for Sobolev Spaces on Open Manifolds

We prove a general embedding theorem for Sobolev spaces on open manifolds of bounded geometry and infer from this the module structure theorem. Thereafter we apply this to weighted Sobolev spaces.     

BIOLOGICAL ACTIVITIES OF PHTHALOCYANINES-X. SYNTHESES AND ANALYSES OF SULFONATED PHTHALOCYANINES

Abstract— Synthetic methods to obtain selectively sulfonated metallo phthalocyanines are compared. Both condensation and direct sulfonation procedures lead to mixtures of mono- to tetrasulfonated products which are resolved by reverse phase liquid chromatography in buffered aqueous-methanol. The proportion of sulfonated derivatives is examined as a function of the starting reagents in the case of the condensation method, and as a function of the temperature and reaction time in the case of the direct sulfonation procedure. The number of sulfonate groups per phthalocyanine molecule is determined by oxidative degradation of the phthalocyanine ring followed by quantitative chromatographic analysis of the sulfophthalamide and phthalamide fragments.     

Analysis of aromatic compounds in gasoline with flow-switching comprehensive two-dimensional gas chromatography

A comprehensive two-dimensional gas chromatography (GC x GC) instrument has been created by coupling a flow-switching modulator and a standard gas chromatograph. The instrument was used to characterize the aromatic composition of gasoline. The high-resolution separation produced by flow-switching GC x GC allowed gasoline aromatics to be fully resolved from saturated components. The aromatic compounds were further separated into groups having the same carbon number. A standard gasoline sample was analyzed to evaluate the quantitative accuracy and precision of this technique. The data show that flow-switching GC x GC produces results that are comparable to gas chromatography-mass spectrometry (GC-MS) and thermal modulation GC x GC. The simple, low-cost, and robust nature of flow-switching GC x GC makes it an ideal technique for the routine analysis of aromatic compounds in gasoline.     

Voltammetric sizing of a sphere.

The size of a glass sphere positioned in the center of a microdisk electrode is determined by using a simple electrochemical procedure and is confirmed, additionally, by a microscopical measurement of the sphere at the time of the electrochemical measurement. The cyclic voltammetric response of the naked electrode and of the electrode with the sphere positioned in its center is recorded over a wide range of scan rates (0.002-1.5 V s(-1)). The size of the sphere is then determined by comparison of the experimental voltammogram with simulations for each individual scan rate.     

Planar Chromatographic Study of Flavonoids and Soyasaponins for Validation of Fingerprints of Desmodium adscendens of Different Origin

JPC – Journal of Planar Chromatography – Modern TLC - The flavonoid and triterpenoid soyasaponin content of the aerial parts of Desmodium adscendens from four geographical origins of...     

Anodic Stripping Voltammetry of Heavy Metals at Nanocrystalline Boron‐Doped Diamond Electrode

Boron‐doped Diamond (BDD) electrode has become one of the important tools for heavy metal detection. By studying some analytical parameters of DPASV method, like deposition time and potential in different electrolyte concentrations (acetate buffer), the conditions for detecting very low metal ion levels (Zn, Cd, Pb, and Cu) could be chosen. Diluted electrolyte (0.01 M buffer) was one of the factors favoring low detection and quantification limits, but its quantification range is short in comparison to more concentrated media. For ?1.7 V deposition potential, the detection of single metal at ppb levels was reached in 60 s deposition time. Understanding different metal‐metal interactions shows the limits to the simultaneous determination of heavy metals at BDD. Quantification was possible for the simultaneous determination of Zn, Cd and Pb despite the overlapping of Zn and Cd peaks. The performance of the BDD was compared with that of another C‐based solid electrode: the glassy carbon electrode (without mercury plating). A lower base line current, wider potential range, higher sensitivity (3 to 5 times higher than GC) and longevity of the material were noticed for the BDD.