ICT integration in mathematics initial teacher training and its impact on visualization: the case of GeoGebra

This case study investigates the impact of the integration of information and communications technology (ICT) in mathematics visualization skills and initial teacher education programmes. It reports on the influence GeoGebra dynamic software use has on promoting mathematical learning at secondary school and on its impact on teachers’ conceptions about teaching and learning mathematics. This paper describes how GeoGebra-based dynamic applets – designed and used in an exploratory manner – promote mathematical processes such as conjectures. It also refers to the changes prospective teachers experience regarding the relevance visual dynamic representations acquire in teaching mathematics. This study observes a shift in school routines when incorporating technology into the mathematics classroom. Visualization appears as a basic competence associated to key mathematical processes. Implications of an early integration of ICT in mathematics initial teacher training and its impact on developing technological pedagogical content knowledge (TPCK) are drawn.     

The Semi-infinite Asymmetric Exclusion Process: Large Deviations via Matrix Products

We study the totally asymmetric exclusion process on the positive integers with a single particle source at the origin. Liggett (Trans. Am. Math. Soc. 213, 237–261, 1975) has shown that the long term behaviour of this process has a phase transition: If the particle production rate at the source and the original density are below a critical value, the stationary measure is a product measure, otherwise the stationary measure is spatially correlated. Following the approach of Derrida et al. (J. Phys. A 26(7), 1493, 1993) it was shown by Grosskinsky (2004) that these correlations can be described by means of a matrix product representation. In this paper we derive a large deviation principle with explicit rate function for the particle density in a macroscopic box based on this representation. The novel and rigorous technique we develop for this problem combines spectral theoretical and combinatorial ideas and is potentially applicable to other models described by matrix products.     

Quadrupole Transitions in the Bound Rotational-Vibrational Spectrum of the Hydrogen Molecular Ion

The three-body Schrödinger equation of the ${{\rm H}_{2}^{+}}$ hydrogen molecular ion is solved in perimetric coordinates using the Lagrange-mesh method. Energies and wave functions of the four lowest vibrational bound or quasibound states for total orbital momenta from 0 to 40 are calculated with high accuracy. A simple calculation using the associated Gauss quadrature provides accurate quadrupole transition probabilities per time unit between those states over the whole rotational bands.     

Cyclometalated AuIII Complexes for Cysteine Arylation in Zinc Finger Protein Domains: towards Controlled Reductive Elimination

With the aim of exploiting the use of organometallic species for the efficient modification of proteins through C-atom transfer, the gold-mediated cysteine arylation through a reductive elimination process occurring from the reaction of cyclometalated Au^III C^N complexes with a zinc finger peptide (Cys₂His₂ type) is here reported. Among the four selected Au^III cyclometalated compounds, the [Au(C^CON)Cl₂] complex featuring the 2-benzoylpyridine (C^CON) scaffold was identified as the most prone to reductive elimination and Cys arylation in buffered aqueous solution (pH 7.4) at 37 °C by high-resolution LC electrospray ionization mass spectrometry. DFT and quantum mechanics/molecular mechanics (QM/MM) studies permitted to propose a mechanism for the title reaction that is in line with the experimental results. Overall, the results provide new insights into the reactivity of cytotoxic organogold compounds with biologically important zinc finger domains and identify initial structure–activity relationships to enable Au^III-catalyzed reductive elimination in aqueous media.     

Quantum parallelism as a tool for ensemble spin dynamics calculations

Efficient simulations of quantum evolutions of spin-1/2 systems are relevant for ensemble quantum computation as well as in typical NMR experiments. We propose an efficient method to calculate the dynamics of an observable provided that the initial excitation is "local." It resorts to a single entangled pure initial state built as a superposition, with random phases, of the pure elements that compose the mixture. This ensures self-averaging of any observable, drastically reducing the calculation time. The procedure is tested for two representative systems: a spin star (cluster with random long range interactions) and a spin ladder.     

Ferrocenyl‐Coupled N‐Heterocyclic Carbene Complexes of Gold(I): A Successful Approach to Multinuclear Anticancer Drugs

Four gold(I) carbene complexes featuring 4‐ferrocenyl‐substituted imidazol‐2‐ylidene ligands were investigated for antiproliferative and antivascular properties. They were active against a panel of seven cancer cell lines, including multidrug‐resistant ones, with low micromolar or nanomolar IC₅₀ (72 h) values, according to their lipophilicity and cellular uptake. The delocalized lipophilic cationic complexes 8 and 10 acted by increasing the reactive oxygen species in two ways: through a genuine ferrocene effect and by inhibiting the thioredoxin reductase. Both complexes gave rise to a reorganization of the F‐actin cytoskeleton in endothelial and melanoma cells, associated with a G1 phase cell cycle arrest and a retarded cell migration. They proved antiangiogenic in tube formation assays with endothelial cells and vascular‐disruptive on real blood vessels in the chorioallantoic membrane of chicken eggs. Biscarbene complex 10 was also tolerated well by mice where it led to a volume reduction of xenograft tumors by up to 80 %.     

Intermolecular Carbonyl–olefin Metathesis with Vinyl Ethers Catalyzed by Homogeneous and Solid Acids in Flow

The carbonyl–olefin metathesis reaction has experienced significant advances in the last seven years with new catalysts and reaction protocols. However, most of these procedures involve soluble catalysts for intramolecular reactions in batch. Herein, we show that recoverable, inexpensive, easy to handle, non-toxic, and widely available simple solid acids, such as the aluminosilicate montmorillonite, can catalyze the intermolecular carbonyl–olefin metathesis of aromatic ketones and aldehydes with vinyl ethers in-flow, to give alkenes with complete trans stereoselectivity on multi-gram scale and high yields. Experimental and computational data support a mechanism based on a carbocation-induced Grob fragmentation. These results open the way for the industrial implementation of carbonyl–olefin metathesis over solid catalysts in continuous mode, which is still the origin and main application of the parent alkene–alkene cross-metathesis.