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?     

Large-scale production of cellulose-binding domains. Adsorption studies using CBD-FITC conjugates

A method for the gram-scale production of cellulose-binding domains (CBD) through the proteolytic digestion of a commercial enzymatic preparation (Celluclast) was developed. The CBD obtained, isolated from Trichoderma reesei cellobiohydrolase I, is highly pure and heavily glycosylated. The purified peptide has a molecular weight of 8.43 kDa, comprising the binding module, a part of the linker, and about 30% glycosidic moiety. Its properties may thus be different from recombinant ones expressed in bacteria. CBD-fluorescein isothiocyanate conjugates were used to study the CBD-cellulose interaction. The presence of fluorescent peptides adsorbed on crystalline and amorphous cellulose fibers suggests that amorphous regions have a higher concentration of binding sites. The adsorption is reversible, but desorption is a very slow process.     

On the sheaf of extendible ideals of topological algebras

In this paper a new sheaf for topological algebras, called the sheaf of extendible ideals, is introduced. It is shown that the sheaf space of this sheaf is uniformizable but not complete in general. The research of both of the authors was supported by Estonian Science Foundation grant 6205.     

Interactions of xanthines with activated carbon: II. The adsorption equilibrium

In the present work, we have studied the adsorption of xanthine derivatives by activated carbon sorbents in aqueous solutions. The study comprised both kinetic, equilibrium and thermodynamic aspects. The kinetic results were reported in a previous paper; the equilibrium-related results are discussed here. The two types of carbon used exhibit some differences but the equilibrium isotherms obtained are all of the H-3 type in the classification of Giles. This suggests a high affinity of the sorbents for the sorbates. We also found that the overall adsorption process comprises more than one individual adsorption-desorption process of which one leads to the formation of a “monolayer” and the other to the “precipitation” of the sorbate on the sorbent surface (multilayer adsorption); the amount of sorbate adsorbed in monolayer form was seemingly greater in C-A14.     

Peptide labeling using 188Re, 188Re-MAG3 and 153Sm-H1ETA: A comparison on their in vitro lipophilicity

Lanreotide peptide was labeled with ¹⁵³Sm-H₁ETA and ¹⁸⁸Re-MAG₃ in order to evaluate whether or not their conjugation to the peptide produce significant differences of the in vitro lipophilicity with respect to the ¹⁸⁸Re-lanreotide prepared by the direct labeling method (highly lipophilic). The differences of lipophilicity between the complexes, were evaluated using a reverse phase HPLC system. The measured lipophilicity of ¹⁵³Sm-H₁ETA-lanreotide, ¹⁸⁸Re-MAG₃-lanreotide and ¹⁸⁸Re-lanreotide was taken to be the capacity factor [k" = (t _R-t ₀)/t ₀ where t _R is the retention time and t ₀ is the dead time] for each of the complexes under identical chromatography conditions. Results showed that the in vitro lipophilicity decreased in the order ¹⁸⁸Re-lanreotide (direct labeling), ¹⁸⁸Re-MAG₃-lanreotide and ¹⁵³Sm-H₁ETA-lanreotide. Since the last one has a capacity factor (k") similar to that of ¹⁸⁸Re-MAG₃, some renal elimination for ¹⁵³Sm-H₁ETA-lanreotide could be expected, which probably would reduce the unnecessary radiation dose to normal tissues.     

Structural Study of Silica Xerogel Composites Containing Pd Aggregates

Composites containing Pd aggregates dispersed in amorphous silica are of interest from both a fundamental and applied point of view because of their attractive catalytic properties. The silica powders added with palladium, prepared by the sol-gel method, were studied using X-ray diffraction, and IR- and UV-Vis-spectrophotometry. Silica xerogel samples were prepared using a ethanol/H₂O/TEOS molar ratio of 4:11.6:1 and loaded with sodium tetrachloropalladate. The silica xerogel microstructure of the powders was studied as a function of annealing temperature. Attention was paid to the evolution of the glass matrix as well as the palladium aggregates in the SiO₂ matrix. We found in our samples partial crystallization of the glass matrix in form of quartz and cristobalite phases with palladium oxide and metallic palladium phase at 1000^∘C. The Rietveld refinement method was used in order to determine the percentage of the phase contents.     

Experimental designs and response surface modeling applied for the optimization of metal-cyanide complexes analysis by capillary electrophoresis

The development of capillary zone electrophoresis (CZE) methods for the determination of metal cyanide complexes in real samples showed some problems, such as the low detection signal of Au (CN)2- and the low resolution between Ni(II) and Fe(II) cyanides in gold processing solutions, and the lack of separation of Pt(CN)4(2-) and Pd(CN)4(2-) in the leachates from automobile catalytic converters. To optimize some analytical parameters, the present study thus focused on the application of experimental designs and multiregression models. The following factors were examined by a two-level factorial design: applied voltage, injection time, detection wavelength, buffer ion, ionic strength and buffer modifiers. For optimization of the CZE method, subsequent response-surface experiments with the important factors were made with the two kinds of leaching solutions. Optimal analytical conditions were obtained in each case, giving good detection signals and resolution for the components of the studied leachates.     

Self-assembled peptide tubelets with 7 A pores

Here we report the preparation and structural characteristics of self-assembling peptide tubelets composed of 32-membered rings formed of alternating alpha-amino acids and cis-3-aminocyclohexanecarboxylic acids. The tubelets possess a partial hydrophobic core environment, provided by the projection of the cyclohexane C2 methylene moiety into the lumen, and a Van der Waals pore diameter of about 7 A.