Promoting mathematical proof from collective argumentation in primary school

The purpose of this research is to promote the construction of mathematical proof from argumentation at the primary level. To show this is a viable instructional strategy at the primary level, we use a teaching experiment methodology and a task related to geometric proof in this research study. To model and analyze the collective argumentation that took place in the classroom, we reconstructed the discussion using the extended Toulmin model. Collective argumentation at the primary level is a valuable opportunity for primary students and their teachers to generate mathematical proof through collaboration.     

The Denef-Loeser Zeta Function is not a Topological Invariant

An example is given which shows that the Denef–Loeserzeta function (usually called the topological zeta function)associated to a germ of a complex hypersurface singularity isnot a topological invariant of the singularity. The idea isthe following. Consider two germs of plane curves singularitieswith the same integral Seifert form but with different topologicaltype and which have different topological zeta functions. Makea double suspension of these singularities (consider them ina 4-dimensional complex space). A theorem of M. Kervaire andJ. Levine states that the topological type of these new hypersurfacesingularities is characterized by their integral Seifert form.Moreover the Seifert form of a suspension is equal (up to sign)to the original Seifert form. Hence these new singularitieshave the same topological type. By means of a double suspensionformula the Denef–Loeser zeta functions are computed forthe two 3-dimensional singularities and it is verified thatthey are not equal.     

Some Area-Diameter Inequalities for Two-Dimensional Lattices

We obtain some inequalities concerning area and diameter of planar convex sets verifying the assumptions of Minkowski's Theorem, establishing the best possible upper bounds for the ratio A/D, (0,2], and for A/D when some lattice points are included.     

Determination of the pesticides fenthion and fenitrothion by flow injection with amperometric detection

The response of a glassy carbon amperometric detector in a flow system was studied. The values of the hydrodynamic variables were optimized. The detector functioned as a “thin-layer” cell. Methods are proposed for the determination of 1.6 × 10^?7?1.6 × 10^?5 Fenthion and 8 × 10^?6? 8× 10^?5 M Fenitrothion in a methanolic acetate-buffered carrier stream. The detection limits were 0.15 and 0.52 μM, respectively.     

Impacts of quantization on the properties of liquid water

The results of classical and quantum simulations of liquid water over a wide range of temperatures are compared to probe the impact of quantization on the properties of liquid water. We show that, when treated quantum mechanically, water molecules have an enhanced probability of accessing nontetrahedral coordination in the local three-dimensional structure. We discuss how this enhanced probability, also called "effective tunneling", is related to the dynamics of the hydrogen-bond breaking and molecular diffusion in the liquid. We explore in detail how local molecular environments affect the manifestation of quantum effects and identify a previously unreported and apparently unique behavior of the quantum mechanical uncertainty of the water molecule as a function of temperature. The nonmonotonic behavior of the quantum mechanical uncertainty with temperature is shown to be due to the notable strength of the water-water interaction in the condensed phase and becomes further evidence of the importance of the water structure in the properties of this ubiquitous liquid.     

Role of hydrogen bonding interactions in directing one-dimensional thiol-assisted growth of silver-based nanofibers

We present evidence, based on scanning and transmission electron microscopy measurements, for the formation of nanofibers from silver-thiol materials treated with water. Mercapto acetic acid, a thiol with a carboxylic acid group at one end, was employed for the experiments presented here. Nanoparticles, with diameters as large as 1 nm, fill the nanofibers and are responsible for absorption bands between 2 and 5.5 eV in UV-visible absorption spectroscopy measurements. The nanofibers disappear at pH values larger than the first pK(a) of the acid, while rods are observed for pH values between 3.6 and 7. This result is interpreted in the context of hydrogen bonding interactions playing an important role in driving the one-dimensional growth of the fibers, a proposal that is supported by the vibrational frequency of the carbonyl stretching mode in surface reflection Fourier transform infrared measurements on dry deposits of aqueous dispersions of the thiol-silver material.     

Photochemical reduction of phenosafranine by edta and its use in amperometric titrations

Phenosafranine in the presence of ethylenediaminetetraacetic acid is reduced to the leuco dye form on illumination with white light. The rate of photoreduction is strongly pH-dependent and exhibits a maximum at about pH 6. Variables such as wavelength and intensity of the light and the concentration of reactants have been studied. The photoreduction involves a long-lived excited state of the dye and is retarded by small amounts of p-phenylenediamine and iodide. The dye is used as an amperometric indicator in titrations of Pb(II), Zn(II) and Cu(II) with EDTA; the method is applicable in the range 0.02–0.0005 M. The current is caused by anodic oxidation of the phenosafranine reduced in the photochemical reaction with EDTA.     

The stereochemistry of pipitzols and perezols

The stereochemistry of α-pipitzol (1a) has been established by transformation to cedrene (4) and by single crystal X-ray diffraction of α-pipitzol benzoate (1b). The stereochemistries of the related cedranolides β-pipitzol (2a), α-(1c), β-(2c) and γ-perezol (1d) are assigned from their respective ORD curves.     

Nonracemic alpha-allenyl carbinols from asymmetric propargylation with the 10-trimethylsilyl-9-borabicyclo[3.3.2]decanes

[reaction: see text] The asymmetric propargylboration of aldehydes at -78 degrees C in <3 h with 1 provides silylated alpha-allenyl carbinols 6 (60-87%) in high ee (94% to >98% ee). The reagents 1 are easily prepared in both enantiomeric forms with a simple Grignard procedure and air-stable borinate complexes 2. The ozonolysis of 6 proceeds smoothly through an acylsilane intermediate to give a TMS ester, which is hydrolyzed to the alpha-hydroxy acid quantitatively with water.