An arithmetic-algebraic work space for the promotion of arithmetic and algebraic thinking: triangular numbers

ZDM – Mathematics Education - This paper presents an experiment that attempts to mobilise an arithmetic-algebraic way of thinking in order to articulate between arithmetic thinking and the...     

Liquid‐Crystalline Thiol‐ and Disulfide‐Based Dendrimers for the Functionalization of Gold Nanoparticles. Preliminary Communication

Liquid‐crystalline dendrons carrying either a thiol or disulfide function which display nematic, smectic A, columnar, or chiral nematic phases have been synthesized. Their mesomorphic properties are in agreement with the nature of the mesogenic units and structure of the dendrons. The first‐generation poly(aryl ester) dendron containing two cyanobiphenyl mesogenic units was used to functionalize gold nanoparticles. For full coverage, a smectic‐like supramolecular organization on the nanometer scale is observed, when the gold nanoparticles are spread onto carbon‐coated copper grids. This result indicates that the dendritic ligands reported here act as self‐organization promoters.     

Comparison of <Emphasis Type="Italic">Yarrowia lipolytica</Emphasis> Lipase Immobilization Yield of Entrapment,Adsorption, and Covalent Bond Techniques

The purpose of this study was to immobilize lipase from Yarrowia lipolytica using three methods including inclusion, adsorption, and covalent bond to study enzyme leaching, storage, and catalytic properties. Sodium alginate and chitosan were the polymers selected to immobilize lipase by inclusion. The beads of each polymer were dried by freeze drying and fluidization. The results show that chitosan was more adapted to the inclusion of lipase. Even though freeze dried, bead activity was low compared to that of fluidized beads. The freeze-drying process seems to produce suitable beads for storage at 4 and 20 degrees C. The immobilization by adsorption was carried out on both celite and silica gel. Maximum immobilization yield of 76% was obtained with celite followed by 43% in silica gel. The enzyme adsorbed on the two supports exhibited greater stability at a certain temperature (50 degrees C) and in no polar solvents (Isooctane, n-heptane, and n-hexane). In addition, the lipase immobilized by covalent bond retained residual activity equitable to 70%. It was demonstrated that the enzyme immobilized by covalent bond showed greater activity (80%) after 5 months of storage.     

Determination of Am and Cm in spent nuclear fuels by isotope dilution inductively coupled plasma mass spectrometry and isotope dilution thermal ionization mass spectrometry after separation by high-performance liquid chromatography

Elemental and isotopic determination of americium and curium in spent nuclear fuels is necessary to validate neutronic calculation codes and for nuclear waste disposal purposes. Prior to mass spectrometric analysis, it is mandatory to perform separations in order to eliminate isobaric interferences between U, Pu, Am and Cm. In the spent fuels samples analyzed, a separation of U and Pu has been first realized with an anion-exchange resin. Then a rapid Am/Cm separation has been developed by high-performance liquid chromatography (HPLC) with an on-line detection using the Am and Cm α-emission. The influence of the different parameters on the chromatographic separation are described and discussed. Inductively coupled plasma mass spectrometry (ICP-MS) and thermal-ionization mass spectrometry (TIMS) have been used to measure the isotopic composition of U, Am and Cm and to determine the ²⁴¹Am/²³⁸U and ²⁴⁴Cm/²³⁸U ratios with the double spike isotope dilution method. The measurement procedures and the accuracy and precision of the results obtained with a quadrupole ICP-MS on different spent fuels samples are discussed and compared with those obtained by TIMS, used as a reference technique. Received: 30 November 1998 / Revised: 8 January 1999 / Accepted: 12 January 1999     

Triblock copolymers in a selective solvent: Dilute and semi-dilute solutions

Triblock copolymers polystyrene-polyisoprene-polystyrene were studied in dilute and semi-dilute solutions in a selective solvent, i.e. a non-solvent for polystyrene and a good solvent for polyisoprene. The mass of the copolymer is equal to 1.6×10⁵g/mol and it contains 70% of polyisoprene. At a concentration C equal to 1.6×10⁻³ g/cm³ triblock aggregation occurs. Experiments performed on dilute solutions¹ plead in favor of loose and polydisperse aggregates rather than spherical micelles: 1) the form factor of the aggregates shows a smooth decrease at qR<1; 2) internal modes are observed by quasi-elastic light scattering; 3) specific viscosity measurements show that the internal concentration of unimers and aggregates are identical; 4) the unimer concentration and the aggregation number depend on the copolymer concentration. In semi-dilute solutions² (C>3×10⁻² g/cm³), dynamical properties are strongly affected by the temperature. Viscosity and longest relaxation time increase by a factor 10⁵ as the temperature decreases from 50°C to 5°C, whereas the plateau modulus G remains independent of the temperature and proportional to the concentration. Small angle neutron scattering experiments reveal a cubic structure having a unit cell dimension d independent of the temperature and varying as C^−1/3 leading to G∼1/d³. Quasi-elastic light scattering experiments performed on this system show a wide relaxation function extending over 7 decades of time. These results argue for a lattice made of polystyrene nodes linked together by the polyisoprene middle blocks, the dynamics being governed by the glass transition of the nodes.     

An insight into tapioca and wheat starch gelatinization mechanisms using TD-NMR and complementary techniques

To provide evidence for previously proposed assumptions concerning starch gelatinization sub-mechanisms, a more detailed investigation was carried out using multiscale analysis of a starch type selected for its marked difference. Tapioca starch was chosen due to its cohesive/springy properties and its growing use in the food industry. Time-domain nuclear magnetic resonance (TD-NMR) was used to investigate the leaching of material, water absorption and crystallite melting in hydrated tapioca starch (45%). The interpretation of T2 mass intensity evolutions, especially those of the (intra- and extra-granular) aqueous phases, was discussed drawing on complementary techniques such as microscopy, Rapid Visco Analyser (RVA), differential scanning calorimetry (DSC) and swelling factor (SF) and solubility index (SI) measurements. Results show that the T2 assignments usually proposed in the literature are dependent on starch origin. The differences in T2 evolutions (value and mass intensity) observed between wheat and tapioca starches at intermediate hydration levels could be linked to the different gelatinization behaviour of tapioca starch involving the latter's higher granule rupture level, higher gelatinization temperature and greater swelling power above its gelatinization temperature.     

Characterization of gluten-free bread crumb baked at atmospheric and reduced pressures using TD-NMR

This research aimed to study the effects of using a partial vacuum for bread baking on macromolecules and water distribution in gluten-free bread. Bread baking under partial vacuum results in greater oven rise and a larger gas fraction in the crumb. Because water's boiling point decreases under reduced pressure, it was expected that its distribution within the dough and its interactions with the others dough's constituents (mainly starch) would differ from those in bread baked under atmospheric pressure. Time-domain nuclear magnetic resonance was used, as it has the rare capacity to quantify both gelatinization and retrogradation of starch. Complementary rheological measurements made it possible to show that crumb Young's modulus was mostly influenced by the gas fraction whereas there was little change in starch gelatinization and retrogradation when dough was baked under partial vacuum. When insufficiently hydrated (48%), the volume of breads was practically the same whatever the baking process. Meanwhile, the nuclear magnetic resonance results suggested that amylose short-term crystallization (on cooling) is dependent on water content. In addition, crumb Young's modulus during storage at room temperature correlated with an increase in free induction decay signal intensity.     

Bubble Solution Description by Non-Extensive Thermodynamics: Pressure Effect

We showed in this study that nanobubble solutions should not be considered as the simple juxtaposition of autonomous phases (a solution and bubbles) but as particular entities, that is, “supersaturated solutions” where gas is simultaneously in two forms in permanent exchange. Gibbs′ extensive thermodynamics cannot claim to describe legitimately their behavior. In this work, we showed how the use of the non-extensive thermodynamics allows describing the physicochemical properties of such media, some of which are counter-intuitive. Thus, an increase in pressure can result in an increase in the bubble size, contrary to what is provided by Boyle-Mariotte's law. The theoretical relationships proposed in this work constitute another approach to bubble solutions, which considers the non-autonomous nature of the components of supersaturated gas solutions and their “non-extensive” nature.     

Synthesis of Bis(arylethynyl)pyrrolo[3,2-b]pyrroles and Effect of Intramolecular Charge Transfer on Their Photophysical Behavior

3,6-Bis(arylethynyl)pyrrolo[3,2-b]pyrroles were synthesized through a two-step procedure involving double direct alkynylation of the electron-rich core followed by Sonogashira coupling. In comparison with the parent tetraarylo-pyrrolo[3,2-b]pyrroles and benzo-fused pyrrolopyrroles, these new dyes showed moderately redshifted absorption. Almost all derivatives showed positive fluorescence solvatochromism and, for the first time, red-emitting pyrrolopyrroles were obtained. Computational studies revealed that, in most cases, there is negligible change in the geometry between ground and excited states. Interestingly, there was a fundamental difference between pyrrolopyrroles possessing electron-withdrawing substituents at positions 2 and 5 and their analogs lacking these substituents. The former dyes behaved like dipolar chromophores with the lowest excited state both one-photon and two-photon allowed, which corresponds to intramolecular charge transfer occurring along the branches perpendicular to the pyrrolopyrrole long axis. In compounds lacking electron-withdrawing substituents at positions 2 and 5, intramolecular charge transfer took place along the long axis of pyrrolopyrrole and consequently the one-photon transitions are not two-photon allowed. Despite displaying quadrupolar core-to-peripheral intramolecular charge transfer, these derivatives showed two-photon absorption cross sections in the NIR1 region comparable to tetraaryl-pyrrolo[3,2-b]pyrroles lacking π-expansion (up to about 500 GM).