Indirect proof: what is specific to this way of proving?

The study presented in this paper is part of a wide research project concerning indirect proofs. Starting from the notion of mathematical theorem as the unity of a statement, a proof and a theory, a structural analysis of indirect proofs has been carried out. Such analysis leads to the production of a model to be used in the observation, analysis and interpretation of cognitive and didactical issues related to indirect proofs and indirect argumentations. Through the analysis of exemplar protocols, the paper discusses cognitive processes, outlining cognitive and didactical aspects of students’ difficulties with this way of proving.     

Glycoside and peptide clustering around the octasilsesquioxane scaffold via photoinduced free-radical thiol-ene coupling. The observation of a striking glycoside cluster effect

Two series of multivalent octasilsesquioxane glyco- and peptido-conjugates were synthesized using the photoinduced free-radical thiol-ene coupling (TEC). The first series was obtained by coupling C-glycosylpropyl thiols and cysteine containing peptides with the known octavinyl octasilsesquioxane while the second series was obtained by reacting glycosyl thiols with a new octasilsesquioxane derivative displaying eight PEGylated chains functionalized with terminal allyl groups. The evaluation of the binding properties of mannoside and glucoside clusters toward Concanavalin A by Enzyme-Linked Lectin Assay (ELLA) revealed a modest glycoside cluster effect. On the other hand, the PEGylated POSS-based glycocluster featuring eight N-acetyl-glucosamine residues showed high affinity toward Wheat Germ Agglutinin to give a measured IC(50) at 3 nM. The calculated relative potency per number of sugar unit (rp/n) was superior to a value of 10(6), thus revealing the occurrence of a striking glycoside cluster effect.     

The control of the growth of Pt clusters in solution: A way to prepare Pt particles of tailored size

The growth of Pt particles in mesitylene-solvated metal atoms, obtained by metal vapour synthesis (MVS), has been followed at two temperatures (−40 and 25 °C) by NMR DOSY technique. The addition of 1,3-divinyltetramethyldisiloxane (DVS) at different time allows to quench the growth process and to make the resulting thermally stable solutions suitable for the evaluation of the Pt particles size at that moment. These solutions can be conveniently used to prepare supported Pt systems containing Pt particles of tailored size.     

Conformational studies by dynamic NMR. 88.(1) stereomutation processes in the diastereoisomers of a representative amino alcohol and related amide precursors

The barriers for three internal motions (i.e., phenyl and tert-butyl rotation as well as N-inversion) have been determined by dynamic NMR spectroscopy in the two diastereoisomeric forms of a typical amino alcohol [dimethylamino-2,4,4-trimethyl-3-phenyl-3-pentanol, Me(2)NCH(2)CHMeC(OH)PhBu(t)]. The two structures were assigned by connection with those of the corresponding amide precursors determined by single-crystal X-ray diffraction. These amides (C=O in place of CH(2)) too were found to undertake internal motions amenable to NMR observation, i.e., phenyl, tert-butyl, and N-CO rotations: the corresponding barriers were also measured. Ab initio computations indicate that H-bonding makes all these molecules adopt six-membered cyclic conformations, a conclusion which agrees well with the X-ray crystal structure determined for the amide precursors.     

A zinc(II)-based receptor for ATP binding and hydrolysis

A protonated Zn(II) complex with a terpyridine-containing pentaamine macrocycle catalyses ATP hydrolysis in the presence of a second metal ion, which acts as cofactor assisting the phosphoryl transfer from ATP to an amine group of the receptor.     

Time-resolved reflectance at null source-detector separation: improving contrast and resolution in diffuse optical imaging

We propose a novel approach to imaging in diffusive media based on time-resolved reflectance measurements at null source-detector separation. This approach yields better spatial resolution and contrast as compared to the classical approach, which typically employs a separation of 20-40 mm. Results are obtained by an analytical perturbation approach to diffusion theory and on Monte Carlo simulations. Practical implementation with state-of-the-art technology and performance of a complementary approach based on the use of small but not null source-detector separation are also discussed.     

Electrostatic interactions effect in the aminolysis of some β‐lactams in the presence of poly(ethyleneimine):structure‐reactivity

The aminolysis reaction of a series of β‐lactams in the presence of poly(ethyleneimine) (PEI) at 30°C and pH = 8.40 has been studied. The substrates investigated follow a pseudo first order rate, except two β‐lactams which show a two step consecutive reaction. Increasing the polyelectrolyte concentration, Michaelis–Menten type kinetics are been observed and for four substrates a more complex rate behaviour was verified owing to the polyelectrolyte inhibition effect. Both the binding constant K₁ between polyelelectrolyte and β‐lactam and the first order rate constant of the reactive complex decomposition k_cat were calculated. The substituent effect at C‐6′ or C‐7′ position of β‐lactam on the aminolysis rate does not correlate with the σ_I value (Taft plot). Most probably, steric and electronic effects are important, but the electrostatic ones are determining factors for the relevant acceleration attributable to both the binding phenomena and the increased reactivity of the substrate–polyelectrolyte complex. The comparison between poly(ethyleneimine) and Human Serum Albumin (HSA) is also discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

A new access to quinazolines from simple anilines

A new synthetic pathway to quinazolines is described. This new method uses hexamethylenetetramine in TFA and potassium ferricyanide in aqueous ethanolic KOH, starting from simple N-protected anilines. The method affords substituted quinazolines with high selectivities and good yields, reducing reaction-time and work-up operations.     

X-Ray and EPR study on copper (II) complexes with an enamine ligand

The enamine (HEAID) obtained from aniline and 2-acetyl-1,3-indandione (2AID) behaves as a bidentate ligand in coordination with copper (II) ion. Two types of crystals, apparently different in shape, were isolated and studied by single-crystal X-ray diffraction. The X-ray data for the brown rhombic crystals of compound 1 shows a mononuclear complex of Cu(II) coordinated with two EAID-anions, Cu(EAID)₂. The X-ray data for the green crystals of compound 2 shows a dinuclear Cu(II) complex with two OH⁻ groups acting as bridging ligands, [Cu₂(μ-OH)₂(EAID)₂]. In both cases the ligand coordinates after deprotonation of the amine group.