An “Instrumental Approach” to Study the Integration of a Computer Tool Into Mathematics Teaching: the Case of Spreadsheets

This article reports on research focused on the integration of a specific computer tool, the spreadsheet, into mathematics teaching. After presenting some important results obtained by research in this area, we revisit these in the light of an instrumental approach, which we perceive as essential to analyse the construction of mathematical meanings in spreadsheet environments and to understand better the questions of technological integration. Then, these theoretical elements are used in order to design an exploratory experiment with grade 7 pupils and analyse its results.     

On the Factorial Closure of Certain Monomial Modules

Abstract

Let R = K[y ₁,…,y _t ] be an affine domain over a field K and I be a nonzero proper ideal of R. In Sec. 1 of this note, we characterize when (K + I, R) is a Mori pair. In Sec. 2 of this note, we prove the following theorem: Let A ? B be domains such that C/Q is Mori for each subring C of B containing A and for any prime ideal Q of C. Then dim A ? 1 ≤ dim B ≤ dim A + 1 and if dim A > 1 or dim B > 1 then dim A = dim B.     

Abraham model correlations for transfer of neutral molecules and ions to sulfolane

Data have been compiled from the published literature on the partition coefficients of solutes and vapors into anhydrous sulfolane. The logarithms of the water-to-sulfolane partition coefficients, log P, and gas-to-sulfolane partition coefficients, log K, were correlated with the Abraham solvation parameter model. The derived correlations described the observed log P and log K values for solutes dissolved in sulfolane to within average standard deviations of 0.14 log units or less. The log P correlation was extended to include the partition of ions by inclusion of a cation-solvent and an anion-solvent term.     

Pharmacophore mapping and electronic feature analysis for a series of nitroaromatic compounds with antitubercular activity

A five point pharmacophore was generated using PHASE for a series of nitroaromatic compounds and their congeners as antitubercular agents. The generated pharmacophore yielded significant 3D‐QSAR model with r² of 0.890 for a training set of 92 molecules. The model also showed excellent predictive power with correlation coefficient Q² of 0.857 for a test set of 31 compounds. The pharmacophore indicated that presence of a nitro group, a piperazine moiety, one aromatic ring feature and two acceptor features are necessary for potent antitubercular activity. The pharmacophore was supported by electronic property analysis using density functional theory (DFT) at B3LYP/3–21*G level. Molecular electrostatic profile of the compounds was consistent with the generated pharmacophore model, particularly appearance of localized negative potential regions near both the oxygen atoms of nitro group extending laterally to the isoxazole ring system/amide bond in the most active compounds. Calculated data further revealed that all active compounds have smaller LUMO energies located over the nitro group, furan ring, and isoxazole ring/amide bond attached to it. Higher negative values of LUMO energies concentrated over the nitro group are indicative of the electron acceptor capacity of the compounds, suggesting that these compounds are prodrugs and must be activated by TB‐nitroreductase. The results obtained from this study should aid in efficient design and development of nitroaromatic compounds as antitubercular agents. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Synthesis with nitriles: synthesis of some new mercaptopyridazine, mercaptopyridazino[1,6-a]quinazoline and thiophene derivatives

2-(1-(4-Bromophenyl)-2-thiocyanatoethylidene)malononitrile (3) undergoes azo coupling with diazotized aromatic amines to afford arylhydrazone derivatives, which are readily cyclized to afford the corresponding 3(2H)-pyridazinimine derivatives upon reflux in aqueous NaOH. Under similar condition an o-cyanoarylhydrazone derivative was cyclized into 6H-pyridazino[1,6-a]quinazolin-6-imine, which in turn was easily transformed into 6H-pyridazino[1,6-a]quinazolin-6-one on reflux in ethanolic/HCl. Compound 3 afforded substituted 5-acetylthiophene derivatives upon reflux in AcOH/HCl mixtures.     

Synthesis and in vitro anticancer activity of some novel tetrahydroquinoline derivatives bearing pyrazol and hydrazide moiety

A new series of tetrahydroquinoline derivatives having pyrazol and hydrazide moieties were synthesized for the purpose of anticancer cell line evaluation. Syntheses of these compounds were firstly achieved by one pot four reactions. The reaction of 3-amino-tetrahydro-1H-pyrazolo [3,4-b]quinolin with aldehydes, indoline-2,3-dione derivatives to give 9a-c , 11a-c , and 13a,b , respectively. In similar manner for biological comparison, the reactions of compound 5 with the same aldehydes and indoline-2,3-dione derivatives to give 19a-c and 20a-c . The newly synthesized compounds were examined in vitro for their cytotoxic activity against HepG-2 and A549 cancer cells. The compounds 11a-c and 20a-c showed promising activity as anticancer agents against HepG-2 and A549 cancer cells.     

Synthesis of libraries of thiazole, oxazole and imidazole-based cyclic peptides from azole-based amino acids. A new synthetic approach to bistratamides and didmolamides

Treatment of a 1 : 1 mixture of the thiazole-based amino acids 8a and 8b with FDPP-i-Pr(2)NEt in CH(3)CN gave a mixture of the cyclic trimers 14, 15, 16 and 17 and the cyclic tetramers 19 and 23 in the ratio 2 : 7 : 5 : 8 : 1 : 1 and in a combined yield of 70%. Separate coupling reactions between the bisimidazole amino acid 45 and the thiazole/oxazole amino acids 43a and 42a in the presence of FDPP-i-Pr(2)NEt led to the bisimidazole based cyclic trimers 55 and 57 respectively (54-57%) and to the cyclic tetramer 56 (8-11%). Similar coupling reactions involving the bisthiazole and bisoxazole amino acids 49 and 47 with the imidazole/oxazole/thiazole amino acids 41a, 42a and 43a gave rise to the library of oxazole, thiazole and imidazole-based cyclic peptides 58, 59, 60, 61, 62, 63, 64 and 65. A coupling reaction between the bisthiazole amino acid 49 and the oxazole amino acid 73 led to an efficient (36% overall) synthesis of bistratamide H (67) found in the ascidian Lissoclinum bistratum. Coupling reactions involving oxazolines with thiazole amino acids were less successful. Thus, a coupling reaction between the phenylalanine-based oxazoline amino acid 71a and either the thiazole amino acid 8a or the bisthiazole amino acid 74 gave only a 2% yield of the cyclic hexapeptide didmolamide A (4) found in the ascidian Didemnum molle. Didmolamide B (68) was obtained in 9% yield from a coupling reaction between 74 and the phenylalanine threonine amino acid 72, using either FDPP or DPPA.