Theory usage and theoretical trends in Europe: a survey and preliminary analysis of CERME4 research reports

The 29th PME research forum on theories included only one European perspective on mathematics education. In order to convey trends in theory usage in Europe we compile, survey and analyze a large subset of the research papers from the 4^th European Congress on Mathematics Education (CERME4). That is, this paper includes a discussion of trends seen within CERME4 reports¹ on theory usage by European researchers inseven of the fourteen working groups and (a) Outlines similarities and differences in theory usage and (b) takes a futuristic stance on ways in which researchers from different traditions could understand each other. Such an enterprise would further Hans-Georg Steiner's vision of bridging theoretical traditions which are independently formulated in different regions of the world.     

A kinematical approach to conformal cosmology

We present an alternative cosmology based on conformal gravity, as originally introduced by H. Weyl and recently revisited by P. Mannheim and D. Kazanas. Unlike past similar attempts our approach is a purely kinematical application of the conformal symmetry to the Universe, through a critical reanalysis of fundamental astrophysical observations, such as the cosmological redshift and others. As a result of this novel approach we obtain a closed-form expression for the cosmic scale factor R(t) and a revised interpretation of the space–time coordinates usually employed in cosmology. New fundamental cosmological parameters are introduced and evaluated. This emerging new cosmology does not seem to possess any of the controversial features of the current standard model, such as the presence of dark matter, dark energy or of a cosmological constant, the existence of the horizon problem or of an inflationary phase. Comparing our results with current conformal cosmologies in the literature, we note that our kinematic cosmology is equivalent to conformal gravity with a cosmological constant at late (or early) cosmological times. The cosmic scale factor and the evolution of the Universe are described in terms of several dimensionless quantitites, among which a new cosmological variable δ emerges as a natural cosmic time. The mathematical connections between all these quantities are described in details and a relationship is established with the original kinematic cosmology by L. Infeld and A. Schild. The mathematical foundations of our kinematical conformal cosmology will need to be checked against current astrophysical experimental data, before this new model can become a viable alternative to the standard theory.     

Rembrandt's Old Woman Praying, 1629/30: A look below the surface using X-ray fluorescence mapping

Rembrandt's painting Old Woman Praying, 1629/30, is the most valuable and exceptional work of art of the Residenzgalerie Salzburg (RGS). It is painted on a gilded copper plate with dimensions of only approximately 15 × 12 cm. The painting probably belongs to a series of three small-scale tronies, all executed on gilded copper plates. This particular picture preparation, which represents a special feature in Rembrandt's work, is quite unusual in the history of art. Previous investigations on the comparable paintings The Laughing Man, 1629/30, in the Mauritshuis, The Hague and the Self Portrait, 1630, in the National Museum, Stockholm showed that the gilding of the copper plate was applied over a lead white ground. To characterize the painting in the RGS, X-ray fluorescence (XRF) mapping was performed in a collaboration between the Research Office Residenzgalerie, Land Salzburg, the XGLab S.R.L, Milan, and the Conservation Science Department of the Kunsthistorische Museum Vienna (KHM). The results indicate a different structure for this painting than that used for The Laughing Man and the Self Portrait. The gilding was applied directly onto the copper plate, but with three areas with the gilding missing. It seems likely that in these sections, the gold was purposely removed to provide a different darker effect. XRF mapping yielded valuable insights into the structure of the painting and its technique as well as the principal pigments used for its composition.     

Scalarizations for adaptively solving multi-objective optimization problems

In this paper several parameter dependent scalarization approaches for solving nonlinear multi-objective optimization problems are discussed. It is shown that they can be considered as special cases of a scalarization problem by Pascoletti and Serafini (or a modification of this problem). Based on these connections theoretical results as well as a new algorithm for adaptively controlling the choice of the parameters for generating almost equidistant approximations of the efficient set, lately developed for the Pascoletti-Serafini scalarization, can be applied to these problems. For instance for such well-known scalarizations as the ε-constraint or the normal boundary intersection problem algorithms for adaptively generating high quality approximations are derived.     

Cooperativity as quantification and optimization paradigm for nuclear receptor modulators

Nuclear Receptors (NRs) are highly relevant drug targets, for which small molecule modulation goes beyond a simple ligand/receptor interaction. NR–ligands modulate Protein–Protein Interactions (PPIs) with coregulator proteins. Here we bring forward a cooperativity mechanism for small molecule modulation of NR PPIs, using the Peroxisome Proliferator Activated Receptor γ (PPARγ), which describes NR–ligands as allosteric molecular glues. The cooperativity framework uses a thermodynamic model based on three-body binding events, to dissect and quantify reciprocal effects of NR–coregulator binding (K^I_D) and NR–ligand binding (K^II_D), jointly recapitulated in the cooperativity factor (α) for each specific ternary ligand·NR·coregulator complex formation. These fundamental thermodynamic parameters allow for a conceptually new way of thinking about structure–activity-relationships for NR–ligands and can steer NR modulator discovery and optimization via a completely novel approach.

A cooperativity framework describes the formation of nuclear receptor ternary complexes and deconvolutes ligand and cofactor binding into intrinsic affinities and a cooperativity factor, providing a conceptually new understanding of NR modulation.     

Improved diffusion Monte Carlo propagators for bosonic systems using Itô calculus

The construction of importance sampled diffusion Monte Carlo (DMC) schemes accurate to second order in the time step is discussed. A central aspect in obtaining efficient second order schemes is the numerical solution of the stochastic differential equation (SDE) associated with the Fokker-Plank equation responsible for the importance sampling procedure. In this work, stochastic predictor-corrector schemes solving the SDE and consistent with It? calculus are used in DMC simulations of helium clusters. These schemes are numerically compared with alternative algorithms obtained by splitting the Fokker-Plank operator, an approach that we analyze using the analytical tools provided by Ito; calculus. The numerical results show that predictor-corrector methods are indeed accurate to second order in the time step and that they present a smaller time step bias and a better efficiency than second order split-operator derived schemes when computing ensemble averages for bosonic systems. The possible extension of the predictor-corrector methods to higher orders is also discussed.     

Determination of 90Sr and 210Pb in deer bone samples by liquid scintillation counting after ion-exchange procedures

This work describes a procedure for the isolation of ⁹⁰Sr and ²¹⁰Pb from deer bones by anion exchange methods and their sequential measurement by LSC. To prevent collection of Pb on the Sr·Spec^® resin we first separated Pb on a Dowex anion exchange column. Sr, which is not held back on the Dowex column, was then purified using Sr·Spec^® resin: first Ca and the Ra isotopes were eluted with 3 M HNO₃ and then Sr was eluted with distilled water. With this 2-steps procedure pure ²¹⁰Pb and ⁹⁰Sr spectra can be achieved. The chemical yield of both steps was determined by ICP-MS. Our ⁹⁰Sr results show satisfying agreement with data obtained by a shorter Sr·Spec^® method and also by the “classical” ⁹⁰Sr determination using fuming nitric acid. Also ²¹⁰Pb results were checked by re-measuring bone samples with already known ²¹⁰Pb activities. Further our method was verified on the reference sample IAEA-A-12.     

Laccase–polyazetidine prepolymer–MWCNT integrated system: Biochemical properties and application to analytical determinations in real samples

Bioelectrochemical properties of Trametes versicolor Laccase (TvL) and Trametes hirsuta Laccase (ThL) immobilized by using polyazetidine prepolymer (PAP) onto multi-walled carbon nanotubes (MWCNTs) screen printed electrode (SPE) surface, have been studied with several redox mediators by cyclic voltammetry (CV). The efficient entrapment of laccase in the PAP layer was confirmed by determination of both kinetic parameters (maximum current and Michaelis–Menten apparent constant) and analytical performances by chronoamperometry. The Laccase-modified MWCNTs electrode provides an effective biosensor for determination of polyphenols and catecholamines in real matrices; performances of the considered biosensors for real samples analysis are also compared and discussed.     

Immobilization of η-cyclopentadienyltris(dimethylamido)zirconium polymerization catalysts on a chlorosilane- and HMDS-modified mesoporous silica surface: a new concept for supporting metallocene amides towards heterogeneous single-site-catalysts

The modification of a mesoporous silica surface with Si(Ind)(CH₃)₂Cl and the immobilization of CpZr(NMe₂)₃ on this surface was studied via IR-spectroscopy. To reduce side reactions, the indenyl-modified silica was reacted with hexamethyldisilazane (HMDS) under IR-control before the CpZr(NMe₂)₃-immobilization. The role of the hydroxyl group protection with HMDS is discussed. The surface modifications have been repeated via Schlenk technique at the same conditions and the surface modifications were studied with ¹³C CP MAS–NMR, ¹H MAS–NMR, elemental-, SEM- and BET-analysis. The surface species of the resulting catalysts are discussed. The precatalysts have been treated with methylaluminoxane (MAO) (Al:Zr (mol:mol)=500:1) and the resulting Zr contents (leaching-effect) are discussed. All catalysts have been tested in ethylene and propylene polymerization.