John Wallis and the French: his quarrels with Fermat,Pascal, Dulaurens,and Descartes

John Wallis, Savilian professor of geometry at Oxford from 1649 to 1703, engaged in a number of disputes with French mathematicians: with Fermat (in 1657–1658), with Pascal (in 1658–1659), with Dulaurens (in 1667–1668), and against Descartes (in the early 1670s). This paper examines not only the mathematical content of the arguments but also Wallis’s various strategies of response. Wallis’s opinion of French mathematicians became increasingly bitter, but at the same time he was able to use the confrontations to promote his own reputation.     

Synthesis of 1,2,3-triazole-fused heterocycles via Pd-catalyzed cyclization of 5-iodotriazoles

A convenient approach toward polycyclic frameworks containing fused 1,2,3-triazoles is described. The synthesis consists of a Cu-catalyzed cycloaddition and an intramolecular Pd-catalyzed direct arylation or Heck reaction, and affords the products in good to excellent yields.     

Ligand-, structure- and pharmacophore-based molecular fingerprints: a case study on adenosine A1, A2A, A2B, and A3 receptor antagonists

FLAP fingerprints are applied in the ligand-, structure- and pharmacophore-based mode in a case study on antagonists of all four adenosine receptor (AR) subtypes. Structurally diverse antagonist collections with respect to the different ARs were constructed by including binding data to human species only. FLAP models well discriminate ??active?? (=highly potent) from ??inactive?? (=weakly potent) AR antagonists, as indicated by enrichment curves, numbers of false positives, and AUC values. For all FLAP modes, model predictivity slightly decreases as follows: A_2BR?>?A_2AR?>?A₃R?>?A₁R antagonists. General performance of FLAP modes in this study is: ligand-?>?structure-?>?pharmacophore- based mode. We also compared the FLAP performance with other common ligand- and structure-based fingerprints. Concerning the ligand-based mode, FLAP model performance is superior to ECFP4 and ROCS for all AR subtypes. Although focusing on the early first part of the A_2A, A_2B and A₃ enrichment curves, ECFP4 and ROCS still retain a satisfactory retrieval of actives. FLAP is also superior when comparing the structure-based mode with PLANTS and GOLD. In this study we applied for the first time the novel FLAPPharm tool for pharmacophore generation. Pharmacophore hypotheses, generated with this tool, convincingly match with formerly published data. Finally, we could demonstrate the capability of FLAP models to uncover selectivity aspects although single AR subtype models were not trained for this purpose.     

Biotransformation of clovane derivatives. Whole cell fungi mediated domino synthesis of rumphellclovane A

Here we describe the biotransformation of clovane derivatives by filamentary fungi Pestalotiopsis palustris and Penicillium minioluteum, and the application of the latter to the synthesis and determination of the absolute configuration of rumphellclovane A (2). Methoxyclovanol (1), a growth inhibitor of the phytopathogen Botrytis cinerea, is metabolised by P. palustris to yield rumphellclovane A (2), a natural compound recently isolated from the gorgonian coral Rumphella antipathies, two new compounds, (1R,2S,5S,8R,9S,10R)-2-methoxyclovane-9,10-diol (5) and (1S,2S,5S,7R,8R,9R)-2-methoxyclovane-7,9-diol (6), hydroxylated in positions not easily accessed by classic synthetic chemistry, and clovanodiols 3 and 4. P. minioluteum is able to selectively transform methoxyclovanol (1) into clovanodiols 3 and 4 and, in turn, lactone 8, the putative intermediate in the above mentioned synthesis of rumphellclovane A (2), into compound 2 via a domino process. The ability of P. minioluteum to carry out the cleavage of ethers on clovane derivatives is also evaluated.     

Preservice Elementary Teachers' Mathematics Content Knowledge and Teacher Efficacy

The purpose of this study was to examine the relationship between mathematics content knowledge and teacher efficacy during an elementary mathematics methods course. A positive moderate relationship between content knowledge and personal teaching efficacy was found, and this relationship was stable during the course. No relationship was found between content knowledge and outcome expectancy. Written artifacts were used to understand and elaborate on these findings. Those data suggest that prior learning experiences may help explain this relationship. Additionally, they suggest that preservice teachers with different levels of content knowledge may attend to different sources of information when making efficacy judgments about teaching.     

Computer simulations of thermo-sensitive microgels: quantitative comparison with experimental swelling data

In this work, a quantitative comparison between experimental swelling data of thermo-sensitive microgels and computer simulation results obtained from a coarse-grained model of polyelectrolyte network and the primitive model of electrolyte is carried out. Polymer-polymer hydrophobic forces are considered in the model through a solvent-mediated interaction potential whose depth increases with temperature. The qualitative agreement between simulation and experiment is very good. In particular, our simulations predict a gradual shrinkage with temperature, which is actually observed for the microgels studied in this survey. In addition, the model can explain the swelling behavior for different contents of ionizable groups without requiring changes in the hydrophobic parameters. Our work also reveals that the abruptness of the shrinkage of charged gels is considerably conditioned by the number of monomeric units per chain. The swelling data are also analyzed with the Flory-Rhener theory, confirming some limitations of this classical formalism.     

Spectroscopic and Electrochemical Study of the Interconversion and Decomplexation of Cobalt(II) Sandwich Polyoxometalates Based on a Dawson-Type Anion

The reaction of the trivacant Dawson polyoxometalate α-[P(2)W(15)O(56)](12-) and the divalent cations Co(2+) is known to form a symmetrically derived sandwich complex of formula ββ-[Co(4)(H(2)O)(2)(P(2)W(15)O(56))(2)](16-) [symbolized as ββ-Co(4)(P(2)W(15))(2)] at low pH (ca. pH 3). We have shown previously that, by a slight modification of the reaction conditions, trinuclear αβ-[(NaOH(2))Co(3)(H(2)O)(P(2)W(15)O(56))(2)](17-) and dinuclear [(NaOH(2))(2)Co(2)(P(2)W(15)O(56))(2)](18-) complexes [symbolized as αβ-NaCo(3)(P(2)W(15))(2) and Na(2)Co(2)(P(2)W(15))(2), respectively] can be synthesized as aqueous-soluble sodium salts. αβ-NaCo(3)(P(2)W(15))(2) is a "lacunary" sandwich complex that can add a Co(2+) cation to form nearly quantitatively an unsymmetrical Dawson tetracobalt sandwich polyoxometalate, αβ-[Co(4)(H(2)O)(2)(P(2)W(15)O(56))(2)](16-) [symbolized as αβ-Co(4)(P(2)W(15))(2)]. Thus, for Co(4)(P(2)W(15))(2), the junctions between the trivacant {P(2)W(15)} subunits and the central tetrameric unit can be either both β type or β and α types. The interconversion between αβ-Co(4)(P(2)W(15))(2) and ββ-Co(4)(P(2)W(15))(2) and the decomplexation process at low pH, leading to the formation of αβ-NaCo(3)(P(2)W(15))(2) and/or Na(2)Co(2)(P(2)W(15))(2), have been followed in aqueous solution at various pH values by electrochemistry, UV-visible absorption spectroscopy, and (31)P NMR spectroscopy.     

Tandem Michael imino–aldol reactions catalyzed by samarium diiodide

Samarium diiodide catalyzes a one-pot procedure allowing to perform sequentially the Michael addition of a ketene silyl acetal on a cyclic ,β-unsaturated ketone, followed by the addition of a glyoxylic or aromatic imine. The presence of a coordinating group on the imine increases the rate of the reaction.     

Synthesis and Anti‐proliferative Activity of N,N′‐bis‐substituted 1,2,4‐Triazolium Salts against Breast Cancer and Prostate Cancer Cell Lines

A series of 1,4‐N,N′‐bis‐substituted 1,2,4‐triazolium bromide salts were synthesized and tested for anti‐proliferative activity. 1,4‐Bis(naphthalen‐2‐ylmethyl)‐1,2,4‐triazolium bromide ( 2 ) showed activity against MDA‐MB‐468 breast cancer and PC‐3 prostate cancer cell lines.     

A practical synthesis of 2,2-difluoro-3-amino-propanoic acid (α,α-difluoro-β-alanine)

Reformatsky reaction of ethyl bromodifluoroacetate with N,N-(dibenzyl)-1H-benzotriazolyl-1-methylamine gave fully protected α,α-difluoro-β-alanine. Hydrogenolysis and hydrolysis furnished α,α-difluoro-β-alanine. Further transformation into N-phthalimido-α,α-difluoro-β-alanine was described.