Generalized integral transform solution for boundary layer flow over a sphere

The generalized integral transform technique is applied to the boundary layer equations for flow over a sphere in their primitive variables. Even though a diffusion-based eigenvalue problem is used, the velocity profile, shear stress and separation point have been calculated with high accuracy. Low-order approximations are shown to be accurate near the surface and the predictions of the separation point is very good. Comparison with finite difference results shows the better convergence behaviour of the integral transform method.     

A cognitive analysis of dragging practises in Cabri environments

Dragging in Dynamical Geometry Software (DGS) is described by introducing a hierarchy of its functions. This is suitable for classifying different attitudes and aims of students who investigate a geometric problem, such as exploring, conjecturing, validating and justifying. Moreover the hierarchy has cognitive features and can be used to describe the twofold modulities namely ascending and descending in which students interact with external representations (e.g. Cabri drawings). Switching from one modality to the other through dragging often allows them to produce fruitful conjectures and to pass from the empirical to the theoretical side of the question. The genesis of such different functions in students does not happen automatically but is the consequence of specific didactical interventions of the teacher in the pupils' apprenticeship of Cabri practises. A worked-out example illustrates the theoretical concepts introduced in the paper.     

Maps Between Complex Hyperbolic Surfaces

We study examples of surjective holomorphic maps between complex hyperbolic surfaces that are not covering maps. The induced homomorphisms on the fundamental groups have infinite kernel, thus are examples of the nonstandard homomorphisms found by Mostow. We also study the singularities of these maps.     

Investigations on the Stability of Plasma Modified Silicone Surfaces

In this work it was investigated the effect of the exposure to different plasmas on the wettability of silicone samples. We have observed that oxygen. argon, and hydrogen glow discharges are quite effective in reducing the water contact angle of such polymer. However, indifferently to efficiency of the treatment, practically all the modified surfaces recovered great part of their original hydrophobicity. We have investigated this hydrophobic recovery using surface energy measurements and theoretical simulations based on the exponential decay of the population of polar groups on the surface. According to our results such recovery can be attributed to the decrease of polar species at the interface water–polymer surface.     

Influence of the starting materials on the catalytic properties of iron oxides

The effect of iron nitrate, sulfate and chloride on the catalytic properties of hematite toward ethylbenzene dehydrogenation has been studied. Iron nitrate has been the best precursor to prepare the catalysts.     

Synthesis of 1H-Cyclopropa[b]naphthalenes via Trapping of o-Benzoquinodimethanes

1H-Cyclopropa[b]naphthalene ( 10a ) and 3-methyl or dimethyl derivatives have been synthesized by interception of appropriately substituted o-quinodimethanes 3 with 1-bromo-2-chlorocyclopropene 5 , and subsequent dehydrohalogenation of the adducts. The o-quinodimethane derivatives 3 in turn were obtained from the diynes 7 via base-induced isomerization to bisallenes 8 and thermal electrocyclic ring closure.     

Comparisons of the interactions between two analytes and two structurally similar chiral stationary phases using high-performance liquid chromatography, suspended-state high-resolution magic angle spinning nuclear magnetic resonance and solid-state nuclear magnetic resonance spectroscopy

A study of the retention behaviour of the enantiomers (R)- and (S)-1,1'-binaphthyl-2,2'-diol as well as (+) and t-)-O,O'-dibenzoyl-tartaric acid was performed using the two chiral stationary phases (CSPs) Kromasil-DMB and Kromasil-TBB. Detailed information about the interactions between the analytes and the two CSPs was obtained from suspended-state HR/MAS transferred NOESY NMR experiments as well as suspended-state HR/MAS 1H NMR titration experiments. Good correlation between the suspended-state HR/MAS NMR experiments and the corresponding HPLC experiments was obtained. This shows that suspended-state HR/MAS NMR as well as solid-state CP/MAS NMR spectroscopy can be used to investigate interactions between stationary phases and analytes under conditions that are similar to those used in HPLC.     

Protonation equilibria of rauwolfia alkaloids in sulfuric acid solutions

The pK_a values for the indole ring protonation equilibria of the Rauwolfia alkaloids, yohimbine, ajmalicine, reserpine and reserpiline have been measured in strongly sulfuric acid solutions. The alkaloids obey the H_I acidity function stablished by Hinman and Lang for indole ring protonation, but they are considerably weaker bases than alkylindoles. Evidences indicating that these compounds behave as carbon bases are reported.     

Toward an understanding of the catalytic role of hydrogen-bond donor solvents in the hetero-Diels-Alder reaction between acetone and butadiene derivative

A detailed theoretical investigation of the catalytic role of hydrogen-bond- (HB-) donor molecules (water, methanol, chloroform, dichloromethane, and chloromethane) in the hetero-Diels-Alder reaction between acetone and N,N-dimethyl-1-amino-3-methoxy-1,3-butadiene is presented. This work extends a previous study (Domingo, L. R.; Andres, J. J. Org. Chem. 2003, 68, 8662) in which the importance of weak HB-donor solvents to catalyze more effectively than solvents with a higher dielectric constant but no HB-donor capability was analyzed. Now, based on density functional theory (DFT) at B3LYP/6-31+G(d) level calculations, different techniques for analyzing the nature of HB interaction, namely, natural bond orbital (NBO) theory, topological analysis of the electron density (atoms in molecules, AIM, theory), and the electron localization function (ELF) and decomposition of the interaction energy between monomers (energy decomposition analysis, EDA), have been applied to understand why only some HB-donor solvents are able to catalyze the reaction. The catalytic effect of the solvent arises from the improved HB-acceptor capability of the oxygen atom at the transition structure (TS) due to the strong polarization of the carbonyl group. The HB acceptor presents three lone pairs (NBO analysis), and the ELF shows an increment of the electronic charge of the lone pairs of 0.50e with respect to the reactant. All solvent molecules form stronger HB interactions at the TS, but only those presenting larger charge-transfer interactions (water, methanol, chloroform) benefit more from the polarization of the carbonyl group than other solvents (dichloromethane, chloromethane) with less "covalent" character.     

Photochemical acetalization of carbonyl compounds in protic media using an in situ generated photocatalyst

Carbonyl compounds are conveniently converted into their corresponding dimethyl acetals in good yields and short reaction times by means of a photochemical reaction in methanol with a catalytic amount of chloranil (2,3,5,6-tetrachloro-1,4-benzoquinone, CA) as the sensitizer. Using aldehydes gives better results than using ketones, which also tend to form enol ethers as side products. These results are similar to those of simple acid-catalyzed acetalization reactions, suggesting the involvement of a photochemically generated acid. On the basis of steady state and laser flash photolysis data the reaction is proposed to involve the in situ generation of a photocatalyst (2,3,5,6-tetrachloro-1,4-hydroquinone, TCHQ) via reaction of CA with the solvent. The acetalization process is initiated by ionization of TCHQ, followed by loss of a proton to the solvent or the carbonyl, which starts a catalytic reaction. The photocatalyst is regenerated via a disproportionation reaction.