Enantioselective catalytic lithiation using a chiral binaphthyl derivative as electron carrier

The lithiation, of the secondary chloride 2, catalyzed by binaphthyl derivatives, i.e. BINAM 4, BINOL 5, BINAP 6, H8-BINAP 7, Tol-BINAP 8, 2,2’-bis(pyrrolidin-1-yl)-1,1’-binaphthalene 9, and 2,2’-dimethyl-1,1’-binaphthalene 11, in the presence of different ketones has been studied, yielding the corresponding alcohol derivatives 3 and 12-16 in moderate to good yields. Binaphthyl derivative 11 has revealed to be very active as catalyst in the lithiation process at room temperature, and has allowed the preparation of the alcohol derivatives with enantioselectivities up to 50%.

Developing pre-service teachers’ noticing of students’ understanding of the derivative concept

This research study examines the development of the ability of pre-service teachers to notice signs of students’ understanding of the derivative concept. It analyses preservice teachers’ interpretations of written solutions to problems involving the derivative concept before and after participating in a teacher training module. The results indicate that the development of this skill is linked to pre-service teachers’ progressive understanding of the mathematical elements that students use to solve problems. We have used these results to make some suggestions for teacher training programmes.

Size-Dependent and Step-Modulated Supramolecular Electrochemical Properties of Catechol-Derived Adlayers at Pt(hkl) Surfaces

The electrochemical reactivity of catechol-derived adlayers is reported at platinum (Pt) single-crystal electrodes. Pt(111) and stepped vicinal surfaces are used as model surfaces possessing well-ordered nanometer-sized Pt(111) terraces ranging from 0.4 to 12 nm. The electrochemical experiments were designed to probe how the control of monatomic step-density and of atomic-level step structure can be used to modulate molecule–molecule interactions during self-assembly of aromatic-derived organic monolayers at metallic single-crystal electrode surfaces. A hard sphere model of surfaces and a simplified band formation model are used as a theoretical framework for interpretation of experimental results. The experimental results reveal (i) that supramolecular electrochemical effects may be confined, propagated, or modulated by the choice of atomic level crystallographic features (i.e.monatomic steps), deliberately introduced at metallic substrate surfaces, suggesting (ii) that substrate-defect engineering may be used to tune the macroscopic electronic properties of aromatic molecular adlayers and of smaller molecular aggregates.

Electrochemical reactions of catechol, methylcatechol and dopamine at tetrahedral amorphous carbon (ta-C) thin film electrodes

The electrochemical reactions of dopamine, catechol and methylcatechol were investigated at tetrahedral amorphous carbon (ta-C) thin film electrodes. In order to better understand the reaction mechanisms of these molecules, cyclic voltammetry with varying scan rates was carried out at different pH values in H2SO4 and PBS solutions. The results were compared to the same redox reactions taking place at glassy carbon (GC) electrodes. All three catechols exhibited quasi-reversible behavior with sluggish electron transfer kinetics at the ta-C electrode. At neutral and alkaline pH, rapid coupled homogeneous reactions followed the oxidation of the catechols to the corresponding o-quinones and led to significant deterioration of the electrode response. At acidic pH, the extent of deterioration was considerably lower. All the redox reactions showed significantly faster electron transfer kinetics at the GC electrode and it was less susceptible toward surface passivation. An EC mechanism was observed for the oxidation of dopamine at both ta-C and GC electrodes and the formation of polydopamine was suspected to cause the passivation of the electrodes.

Students’ understanding of the function-derivative relationship when learning economic concepts

The aim of this study is to characterise students’ understanding of the function-derivative relationship when learning economic concepts. To this end, we use a fuzzy metric (Chang 1968) to identify the development of economic concept understanding that is defined by the function-derivative relationship. The results indicate that the understanding of these economic concepts is linked to students’ capacity to perform conversions and treatments between the algebraic and graphic registers of the function-derivative relationship when extracting the economic meaning of concavity/convexity in graphs of functions using the second derivative.

Sensitivity Analysis in Convex Optimization through the Circatangent Derivative

The main goal of this paper is to analyse the sensitivity of a vector convex optimization problem according to variations in the right-hand side. We measure the quantitative behavior of a certain set of Pareto optimal points characterized to become minimum when the objective function is composed with a positive function. Its behavior is analysed quantitatively using the circatangent derivative for set-valued maps. Particularly, it is shown that the sensitivity is closely related to a Lagrange multiplier solution of a dual program.