Comparing adult mathematical literacy with PISA students: results of a pilot study

In Germany, very little empirical data about the mathematical competence of adults is available. The aim of this study is to test the level of mathematical competence in an adult sample. For this purpose, a mathematics test was constructed using the PISA mathematics framework as a guideline. The test consisted of fourteen public items from the mathematics test in PISA 2000. The study was implemented by carrying out house visits (Germany). The sample was comprised of 64 adults (90% women, age: 41 years). The test results were scaled in the metric of PISA 2000. Compared with the average German student competencies in PISA 2000, the average competency in the adult sample was on the same level as the fifteen-year-old comprehensive secondary school student (at a German Gymnasium). Further analysis shows that the mathematics competency level in the adult sample is positively connected to the individual vocational education degree.     

Fluorescence from the second excited singlet state of [18] annulenes

The emission spectra of the second excited singlet state of [18] annulene and of monofluoro [18] annulene (in a 3-methylpentane glass at 4 K) are reported. The large energy gap between the first and second excited singlet states inhibits fast internal conversion and favours the appearance of S₂ → S₀ emission. In addition, fluorescence from the S₁ state can be observed in monofluoro [13] annulene by exciting into the S₂ or directly into the S₁ absorption.     

Mechanism of phosphorus-carbon bond cleavage by lithium in tertiary phosphines. An optimized synthesis of 1,2-Bis(phenylphosphino)ethane

Conditions influencing the extent of P-C(aryl) vs P-C(alkyl) bond cleavage in the reaction of Ph(2)P(CH(2))(2)PPh(2) with lithium in THF have been investigated. The results complement and elucidate earlier work; they indicate that the mechanism of P-C bond cleavage in tertiary phosphines of this type involves a thermodynamic equilibrium between P-C(aryl) and P-C(alkyl) cleaved radicals and anions, followed by reaction and stabilization of these as lithium salts. The addition of water to the reaction mixture causes a reestablishment of the cleavage equilibrium prior to the formation of the secondary phosphines. A mechanism involving competitive release of leaving groups as the thermodynamically most stable anion or radical has been proposed. The preparation of (R, R)-(+/-)/(R, S)-PhP(H)(CH(2))(2)P(H)Ph by this route has been optimized.     

Matrix-assisted laser desorption/ionization mass spectrometry with additives to 2,5-dihydroxybenzoic acid

Selected benzoic acid derivatives and related substances were used as additives to 2,5-dihydroxybenzoic acid (2,5DHB) and the performance of the mixtures in matrix-assisted laser desorption/ionization mass spectrometry was investigated. Using benzoic acid derivatives substituted at position 2 and/or 5 or related substances as a co-matrix in the 1–10% range with 2,5DHB results in improved ion yields and signal-to-noise ratio of analyte molecules, especially for the high-mass range. The enhanced performance is prominent for 2-hydroxy-5-methoxybenzoic acid and exists for both proteins and oligosaccharides. It is suggested that the improvement is caused by a disorder in the 2,5DHB crystal lattice allowing ‘softer’ desorption. Charge transfer from matrix ions to additive molecules at the expense of analyte ionization gives a simple explanation for the deteriorating effects of some tested additives.     

Periodic table of the elements and the Thomas–Fermi atom

How the monotonic trend on which the periodicity of the periodic system is superposed is well described by Thomas–Fermi theory is explained. The mathematical structure of the periodicity is elucidated and explained. Algebraic formulas for the key atomic numbers are derived, e.g., the atomic number at which l electrons first appear is given by Z_f(??) = 4 (∑ n²)+1.     

Ab initio SCF Calculation of the Fluoronium Ion: Geometry,electronic structure and vibrational constants

An ab initio SCF calculation of 42 points of the energy hypersurface of the fluoronium ion is presented using a contracted F(5s/3p), H(2s) gaussian basis set. In its equilibrium structure a bond length of 1.812 a.u. and a HFH bond angle of 127.2° are predicted. The calculated vibrational frequencies for H₂F⁺, HDF⁺, and D₂F⁺ are in good agreement with the experimental data.     

Quantum groups in the higgs phase

In the Higgs phase we may be left with a residual finite symmetry groupH of the condensate. The topological interactions between the magnetic and electric excitations in these so-called discreteH gauge theories are completely described by the Hopf algebra or quantum groupD(H). In 2+1 dimensional space time we may add a Chern-Simons term to such a model. This deforms the underlying Hopf algebraD(H) into the quasi-Hopf algebraD (H) by means of a 3-cocycle onH. Consequently, the finite number of physically inequivalent discreteH gauge theories obtained in this way are labelled by the elements of the cohomology groupH ³(H,U(1)). We briefly review the above results in these notes. Special attention is given to the Coulomb screening mechanism operational in the Higgs phase. This mechanism screens the Coulomb interactions, but not the Aharonov-Bohm interactions.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98. No. 3, pp. 509–523, March, 1994