Mathematical problem solving: an evolving research and practice domain

Research programs in mathematical problem solving have evolved with the development and availability of computational tools. I review and discuss research programs that have influenced and shaped the development of mathematical education in Mexico and elsewhere. An overarching principle that distinguishes the problem solving approach to develop and learn mathematics is to conceptualize the discipline as a set of dilemmas or problems that need to be explored and solved in terms of mathematical resources and strategies. In this context, relevant questions that help structure and organize this paper include: What does it mean to learn mathematics in terms of problem solving? To what extent do research programs in problem solving orient curricular proposals? What types of instructional scenarios promote the students’ development of mathematical thinking based on problem solving? What type of reasoning do students develop as a result of using distinct computational tools in mathematical problem solving?     

Hypotheses sur la formation par pyrolyse du premier intermediaire a silicium digonal

The synthesis of 2,8-dimethyl 3,9-dichloro 6-sila[5.5] spiro undecatetra 2.4,8,10-ene is described. The thermal decomposition of the adduct formed by the reaction of this product with methyl acetylene dicarboxylate is studied. From the characterization of the copyrolysis products, two possible mechanisms are proposed which imply the formation of digonal silicon such as 2-silaallene and 2-silaketene.     

BV periodic solutions of an evolution problem associated with continuous moving convex sets

This paper is concerned with BV periodic solutions for multivalued perturbations of an evolution equation governed by the sweeping process (or Moreau's process). The perturbed equation has the form –DuN _C (t)(u(t))+F(t,u(t)), whereC is a closed convex valued continuousT-periodic multifunction from [0,T] to ^d ,N ^C (t)(u(t)) is the normal cone ofC(t) atu(t),F: [0,T]× ^{d d} is a compact convex valued multifunction and Du is the differential measure of the periodic BV solutionu. Several existence results for this differential inclusion are stated under various assumptions on the perturbationF.     

Spectroscopic properties of the photoproducts of pyridoxal-5′-P irradiation: Catalytic site recognition of ribonuclease A

Photoproducts of pyridoxal-5-P, i.e., 4-pyridoxic-5-P and bis-pyridoxal-5-P, have been studied by spectroscopic methods. The spectroscopic properties of bis-pyridoxal-5-P (bis-PLP) resemble those of pyridoxal-5-P (PLP) under similar experimental conditions. The coupling of methylen hydrogens to the phosphorus atom has been shown by NMR spectroscopy. The singlet in the³¹P-NMR spectra and the triplet in¹H-undecoupled experiments confirm the presence of the phosphate group in the 5 position of the structure of the vitamin. The effect of pH and solvent composition on the relative distribution of species of bis-pyridoxine-5-P (bis-PNP) has been investigated by absorption and fluorescence spectroscopy. The acid-base dissociation of the phosphate group is easily detected by emission spectroscopy. Bis-PNP and bis-PLP bind to the enzyme RNase A and they behave as competitive inhibitors with respect to the substrate cytidine-2-3-cyclic phosphate. The natural forms of vitamin B₆, pyridoxine, and pyridoxine-5-P have no effect on the catalytic activity of the protein. Experimental evidence derived from fluorescence and inhibition experiments is consistent with the hypothesis that bis-PNP recognizes the catalytic site of RNase A.     

Synthesis, crystal structure, and properties of MnNCN, the first carbodiimide of a magnetic transition metal

Synthesis, single-crystal structure determination, and magnetic properties are reported for manganese carbodiimide, MnNCN. The presumably unstable but inert phase adopts the trigonal system (R3m) with a = 3.3583(4) A, c = 14.347(2) A, V = 140.13(3) A3, and Z = 3. Divalent manganese is octahedrally coordinated by nitrogen atoms at 2.26 A, and the NCN(2-) unit adopts the linear [N=C=N](2-) carbodiimide shape with two C=N double bonds of 1.23 A. MnNCN contains high-spin Mn(II) with five unpaired electrons and behaves like an antiferromagnet with an ordering temperature below 30 K.     

A LASER FLASH SPECTROSCOPY STUDY OF THE KINETICS OF ELECTRON TRANSFER FROM SPINACH PHOTOSYSTEM I TO SPINACH AND ALGAL FERREDOXINS

Laser flash absorption spectroscopy has been used to investigate the kinetics of electron transfer from P700 in Photosystem I (PSI)-enriched particles from spinach to the ferredoxins from spinach and the green alga Monoraphidium braunii. Very similar behavior for the interaction of both ferredoxins with the PSI complex was observed, although the algal ferredoxin appears to be slightly more effective as an electron acceptor. For both proteins, a non-linear protein concentration dependence of the rate constant for reduction was obtained, indicating complex formation preceding electron transfer. Estimates of 3 times 10⁷M^?1 s^?1 and 140–180 s^?l were obtained from these data for the second order rate constants for complex formation, and the limiting first order rate constants for electron transfer, respectively. At neutral pH, a biphasic dependence of the rate constant for ferredoxin reduction on the concentration of NaCl or MgCl₂ was observed. This was interpreted in terms of the electrostatic interactions which occur between ferredoxin and the PSI membrane. In addition, magnesium cations appear to play a specific role in the interaction between PSI and ferredoxin. Thus, the addition of these ions under optimal conditions induces a 6-f-old increase in the electron transfer reaction rate constant, compared with a 2-f-old increase in the presence of an optimal amount of NaCI. This cannot be explained as arising from ionic strength effects. To our knowledge, this is the first time that a direct measurement of the rate constant for the reduction of ferredoxin by the PSI complex has been reported.     

2,4,6‐Trimethylphenyl isocyanide

The title compound, C₁₀H₁₁N, displays a crystallographic mirror plane that incorporates all the non‐H atoms, as well as the H atoms attached to the aromatic ring. The iso­cyano group is almost linear and shows an N[triple‐bond]C bond distance of 1.158 (3) Å.     

Synthesis of 4-aryl-2,3,6,7-tetrahydro-1H-pyrimido[4,5-b][1,4]-diazepin-6-ones from 4,5-diamino-1H-pyrimidin-6-ones and 1-aryl-3-(dimethylamino)-1-propanones

The reaction of 1-aryl-3-(dimethylamino)-1-propanones 1 with one equivalent of 4,5-diamino-1H-pyrimidin-6-ones 2 , in acidic medium, leads to the formation of 4-aryl-2,3,6,7-tetrahydro-1H-pyrimido[4,5-b]-[1,4]diazepin-6-ones 3 . The structure elucidation of the products is based on detail nmr analysis of experiments such as ¹³C, ¹H and DEPT including selective ¹³C{¹H} decoupling experiments.     

Chemistry of polybutadiene—iron carbonyl systems

The treatment of polybutadienes with iron carbonyls results in formation of polymers containing tricarbonyl(conjugated diene)iron units [C₈H₁₂Fe(CO)₃] and also results in geometrical isomerization of free double bonds. Heating of the iron carbonyl-containing polymers gives ferromagnetic products with enhanced thermal stability. The incorporation of iron carbonyl groups into the polymer is favored by basic solvents and high temperatures, the geometrical isomerization by acidic solvents and low temperatures. Steric factors are powerful in determining the rate of isomerization.     

Structural analysis of metal interactions with the dinucleotide duplex, dCG x dCG, using ion mobility mass spectrometry

The metal binding properties of the dinucleotide duplex, dCG x dCG, were analyzed in the gas phase with ion mobility mass spectrometry. Both MALDI and ESI were used to generate [M(dCG x dCG)]+ complexes. The collision cross section of each complex was measured in helium using ion mobility based methods and compared to calculated cross sections of theoretical structures. When metal cations classified as hard acids were combined with dCG x dCG, the [M(dCG x dCG)]+ complex organized into a globular structure. However, when soft acid metal cations were examined, a structure was observed where the two C-G base pairs were Watson-Crick bound.