De novo synthesis of brominated dioxins and furans by thermogravimetry

Support for this work was provided by the Generalitat Valenciana (Spain) with projects PROMETEO/2009/043/FEDER, and by the Spanish MCT CTQ2008-05520.

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.

Thermogravimetry and Py–GC/MS techniques as fast qualitative methods for comparing the biochemical composition of Nannochloropsis oculata samples obtained under different culture conditions

Microalgae have many applications, such as biodiesel production or food supplement. Depending on the application, the optimization of certain fractions of the biochemical composition (proteins, carbohydrates and lipids) is required. Therefore, samples obtained in different culture conditions must be analyzed in order to compare the content of such fractions. Nevertheless, traditional methods necessitate lengthy analytical procedures with prolonged sample turn-around times. Results of the biochemical composition of Nannochloropsis oculata samples with different protein, carbohydrate and lipid contents obtained by conventional analytical methods have been compared to those obtained by thermogravimetry (TGA) and a Pyroprobe device connected to a gas chromatograph with mass spectrometer detector (Py–GC/MS), showing a clear correlation. These results suggest a potential applicability of these techniques as fast and easy methods to qualitatively compare the biochemical composition of microalgal samples.

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.