Leçons de Mathématiques générales

Monatshefte für Mathematik -     

Two-step photoionization of Na2: dependence on alignment

Laser light is used for two-step photoionization of Na₂. the first step depends on the moleculer orientation, the second step doesnot. This yields a method for the analysis of molecular alignment.     

Operation of KrF and ArF tunable excimer lasers without Cassegrain optics

A commercial tunable excimer laser consists of an oscillator-amplifier combination. The oscillator produces high-quality light that is sent to the amplifier and is distributed throughout the amplifier cavity via Cassegrain optics. We describe here two alternative approaches, a single-pass configuration for use with KrF and a triple-pass configuration with ArF, both of which do away with the Cassegrain optics. In each approach, the beam energy is the same as with Cassegrain optics. For KrF, the changes provide better locking, a higher degree of linear polarization, and a better spatial beam homogeneity, but a poorer beam divergence. For ArF, there is also better beam homogeneity, but the locking efficiency and divergence are not as good as with Cassegrain optics.     

Soft X-Ray Spectromicroscopy Investigation of the Interaction of Aquatic Humic Acid and Clay Colloids

Sub-micrometer-sized anionic polystyrene latices have been coated with uniform layers of iron compounds by aging, at elevated temperature, dispersions of the polymer colloid in the presence of aqueous solutions of ferric chloride, urea, hydrochloric acid, and polyvinylpyrrolidone. The thickness of the deposited layers could be altered by suitable adjustment of the reactant concentrations, and they could also be increased by further aging of the coated particles in the presence of aqueous solutions of ferric chloride. Hollow colloidal spheres of iron compounds were obtained by calcination of the so-coated polystyrene latices at elevated temperature in air. Different chemical compositions of hollow colloidal spheres were obtained by heating them in hydrogen. Copyright 2000 Academic Press.     

Determination of molecular mass, Stokes' radius, frictional coefficient and isomer-type of non-denatured proteins by time-dependent pore gradient gel electrophoresis

Molecular mass, Stoke's radius, frictional coefficient and isomer-type of non-denatured proteins can be obtained by time-dependent gradient gel electrophoresis by evaluating the resulting data using a two-step mathematical procedure. Provided a histochemical staining procedure is available to locate the position of an enzyme in the gel, crude cell extracts can be used for estimating their molecular size properties. The computation of molecular properties of non-denatured proteins is demonstrated for isozymes of aspartate aminotransferase (EC 2.6.1.1), peroxidase (EC 1.11.1.42) and glucose-6-phosphate dehydrogenase (EC 1.1.1.49) from current-year needles of spruce. The resulting data as well as those which were calculated for esterase (EC 3.1.1.1), glutamate dehydrogenase (EC 1.4.1.4), isocitrate dehydrogenase (EC 1.4.1.42), and shikimate dehydrogenase (EC 1.1.1.25) are in accordance with those reported in the literature. The method described may be applied to various scientific areas such as genetics or environmental pollution. It could be shown here that current-year needles of injured spruce (damage class 3) contained two more peroxidase isozymes and one more glucose-6-phosphate dehydrogenase isozyme than those from non-injured trees. These differences may mark two genotypes of spruce of different susceptibilities towards present-day air and soil pollutants.     

Carbazole compounds as host materials for triplet emitters in organic light-emitting diodes: polymer hosts for high-efficiency light-emitting diodes

A carbazole homopolymer and carbazole copolymers based on 9,9'-dialkyl-[3,3']-bicarbazolyl, 2,5-diphenyl-[1,3,4]-oxadiazole and 9,9-bis(4-[3,7-dimethyloctyloxy]phenyl)fluorene were synthesized and their electrical and photophysical properties were characterized with respect to their application as host in phosphorescent polymer light-emitting diodes. It is shown that the triplet energy of a polymer depends on the specific connections between its building blocks. Without changing the composition of the polymer, its triplet energy can be increased from 2.3 to 2.6 eV by changing the way in which the different building blocks are coupled together. For poly(9-vinylcarbazole) (PVK), a carbazole polymer often used as host for high-energy triplet emitters in polymer light-emitting diodes, a large hole-injection barrier of about 1 eV exists due to the low-lying HOMO level of PVK. For all carbazole polymers presented here, the HOMO levels are much closer to the Fermi level of a commonly used anode such as ITO and/or a commonly used hole-injection layer such as PEDOT:PSS. This makes high current densities and consequently high luminance levels possible at moderate applied voltages in polymer light-emitting diodes. A double-layer polymer light-emitting diode is constructed comprising a PEDOT:PSS layer as hole-injection layer and a carbazole-oxadiazole copolymer doped with a green triplet emitter as emissive layer that shows an efficacy of 23 cd/A independent of current density and light output.     

Investigation of polynuclear Zr(IV) hydroxide complexes by nanoelectrospray mass-spectrometry combined with XAFS

Polynuclear species of zirconium in acidic aqueous solution are investigated by combining X-ray absorption spectroscopy (XAFS) and nanoelectrospray mass spectrometry (ESI-MS). Species distributions are measured between pH_C 0 and pH_C 3 for [Zr] = 1.5–10 mM. While the monomer remains a minor species, with increasing pH the degree of polymerization increases and the formation of tetramers, pentamers, octamers, and larger polymers is observed. The high resolution of the mass spectrometer permits the unambiguous determination of polynuclear zirconium hydroxide complexes by means of their isotopic patterns. The relative abundances of mononuclear and polynuclear species present simultaneously in solution are measured, even if one of the species contributes only 0.1% of the Zr concentration. For the first time it has been directly observed that the hydrolysis of polynuclear Zr species is a continuous process which leads to charge compensation through the sequential substitution of water molecules by hydroxide ligands until doubly charged polymers dominate at conditions (H⁺ and Zr concentrations) close to the solubility of Zr(OH)₄(am). The invasiveness of the electrospray process was minimized by using very mild declustering conditions, leaving the polynuclear species within a solvent shell of approximately 20 water molecules. Figure Schematic Diagram of Multiplexed Measurement of 9 Anti-Nuclear Antibodies Using the AtheNa Multilyte Assay