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.     

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     

Chromium-mediated aldol and homoaldol reactions on solid support directed towards an iterative polyol strategy

Chromium-Reformatsky and chromium-homoaldol reactions run under neutral and mild reaction conditions. They are highly chemoselective, tolerant towards most common functional groups, and are not prone to retroaldol reactions. Initial studies directed to transfer these homogeneous chromium-mediated solution-phase reactions to solid phase are presented. The main objective was to develop a methodology to aid a combinatorial iterative strategy to polyols (polyketides) on solid phase. A general reactivity problem was observed with polystyrene based resins compared to the solution-phase reactions, independent if the electrophilic (aldehyde) or nucleophilic (bromide) end of the polyol chain was supported to the resin. A complicated penetration, or loss of the polar solvent environment after penetration into the resin, might be responsible for the reduced reactivity. Application of either a soluble polystyrene resin or a polystyrene resin with a polar polyethylene glycol tether resulted in improved yields.     

Theoretical study on geometry and spectroscopic properties of 1,1′-binaphthyl in the electronic ground and first excited singlet states

Equilibrium geometries for the electronic ground and first excited singlet states of 1,1'-binaphthyl have been calculated by minimization of the total energy with respect to all internal coordinates. Using these results, an interpretation of the fluorescence S₁→ S₀ and absorption spectra S_m ← S₀ and S_n ← S₁ in rigid and fluid solutions is given.For the first time the equilibrium geometry of the first excited singlet state of 1, 1′-binaphthyl has been calculated. On excitation to the S₁ state the dihedral angle θ between the two naphthalene moieties is de- creased from 61 ° to 41 °. A detailed survey of CH bond lengths in the S₀ and S₁ states has been given. This result should be of particular importance for the theoretical treatment of radiationless transitions.Using equilibrium geometries for the S₀ and S₁ states a satisfactory interpretation of the S_m ← S₀ and S_n ← S₁ absorption spectra as well as of the fluorescence spectra in fluid and rigid solutions can be given. Concerning the S_n ← S₁ absorption spectrum in fluid solution, the calculations predict a strong absorption (A ← B transition) in the still uninvestigated region of energies lower than 11000 cm^?1.From the results of this paper and of other calculations it can be concluded that the Warshel-Karplus method yields reliable equilibrium geometries for electronic ground and excited states of unsaturated hydrocarbons [22,23].