Designing a duo of material and digital artifacts: the pascaline and Cabri Elem e-books in primary school mathematics

This paper focuses on a duo of artifacts, constituted by a physical artifact and its digital counterpart. It deals with the theoretically and empirically underpinned design process of the digital artifact, the e-pascaline developed with Cabri Elem technology, in reference to a physical artifact, the pascaline. The theoretical frameworks of the instrumental approach and the theory of semiotic mediation together with the analysis of teaching experiments with the pascaline support the design in terms of continuity and discontinuity between the two artifacts. The components of the digital artifact were chosen from among the components of the physical artifact that are the object of instrumental genesis by the students and that are analyzed as having a semiotic potential that contributes to didactical aims. Components instrumented by students which had inadequate semiotic potential were eliminated. With the resulting duo, each artifact adds value to the use of the other artifact for mathematical learning.     

Fields of moduli and fields of definition of odd signature curves

Let X be a smooth projective curve of genus ${g \geq 2}$ defined over a field K. We show that X can be defined over its field of moduli K _X if the signature of the covering ${X \rightarrow X/ Aut(X)}$ is of type ${(0;c_1,\dots,c_k)}$ , where some c _i appears an odd number of times. This result is applied to cyclic q-gonal curves and to plane quartics.     

Carbohydrate amino acids: the intrinsic conformational preference for a beta-turn-type structure in a carbopeptoid building block

Infrared ion-dip spectroscopy coupled with DFT and ab initio calculations are used to establish the intrinsic conformational preference of the basic structural unit of a peptide mimic, a cis-tetrahydrofuran-based "carbopeptoid" (amide-sugar-amide), isolated at low temperature in the gas phase. The carbopeptoid units form a beta-turn-type structure, stabilized by an intramolecular NH --> O=C hydrogen bond across the sugar ring, thus forming a 10-membered, C10 turn. Despite the clear preference for C10 beta-turn structures in the basic unit, however, the presence of multiple hydrogen-bond donating and accepting groups also generates a rich conformational landscape, and alternative structures may be populated in related molecules. Calculations on an extended, carbopeptoid dimer unit, which includes an alternating amide-sugar-amide-sugar-amide chain, identify conformers exhibiting alternative hydrogen-bonding arrangements that are somewhat more stable than the lowest-energy double beta-turn forming conformer.     

Pressure effects on lipidic direct phases: the dodecyl trimethyl ammonium chloride-water system

The direct lyotropic polymorphism of dodecyltrimethylammonium chloride (DTAC) was investigated by synchrotron X-ray diffraction at different water concentrations under compression up to 2 kbar, i.e., in the pressure intermediate range where interesting biophysical transformations occur and the functional characteristics of cell membranes are altered. The results show that pressure induces the transition from the hexagonal phase to the micellar Pm3n cubic phase in hydrated samples (c between 0.5 and 0.6, c being the weight concentration of lipid in the mixture) and the transition from the bicontinuous Ia3d cubic phase to the hexagonal phase in drier samples (c = 0.8). By increasing the pressure on very dry samples, a lamellar L(alpha) phase was observed to form transitorily at the Ia3d cubic-hexagonal phase transition. Phase compressibility and then the lipid and water partial molecular compressibilities were derived as a function of pressure and concentration. As a result, we assessed the very low compressibility of the hydration water within the lipid phases, and we demonstrated that the compressibility of DTAC is very dependent on pressure. Moreover, the molecular parameters of DTAC calculated in the different phases during compression confirmed that pressure induces small but continuous conformational changes, definitely different from the large changes observed in lipid molecules forming type II structures.     

Synthesis and characterization of a persistent paramagnetic rotaxane based on alpha-cyclodextrin

The synthesis and spectroscopic properties of a novel paramagnetic [2]rotaxane is described. This rotaxane is made from molecules having an alkyl chain flanked by 2,2,6,6-tetramethylpiperidine-N-oxyl (TEMPO) groups. Complexation of sebacoyl chloride by alpha-cyclodextrin followed by reaction with a bulky aminonitroxide resulted in the trapping of the cyclodextrin, threaded by the alkyl chain, thus generating the rotaxane structure. The structure of the paramagnetic [2]rotaxane was fully characterized by ESI-MS, 1D and 2D NMR and ESR spectroscopy.     

Uniqueness and decay estimates for a class of parabolic partial differential equations with hysteresis and convection

We deal in detail with the question of existence, uniqueness and asymptotic behaviour of solutions to a parabolic equation with hysteresis and convection. This equation is part of a model system which describes the magnetohydrodynamic (MHD) flow of a conducting fluid between two ferromagnetic plates. The result of this paper complements the content of a previous paper of the first author, where existence of the solution has been proved under fairly general assumptions on the hysteresis operator and the uniqueness was only obtained for a restricted class of hysteresis operators.     

The proteome of lentil (Lens culinaris Medik.) seeds: Discriminating between landraces

Lentil (Lens culinaris Medik.) is one of the most ancient crops of the Mediterranean region used for human nutrition; an extensive differentiation of L. culinaris over millennia has resulted in a number of different landraces. As a consequence of environmental and socio‐economic issues, the disappearance of many of them occurred in more recent times. To investigate the potential of proteomics as a tool in phylogenetic studies, testing the possibility to identify specific markers of different plant landraces, 2‐D gel electrophoretic maps of mature seeds were obtained from seven lentil populations belonging to a local ecotype (Capracotta) and five commercial varieties (Turca Rossa, Canadese, Castelluccio di Norcia, Rascino and Colfiorito). 2‐DE analysis resolved hundreds of protein species in each lentil sample, among which only 122 were further identified by MALDI‐TOF PMF and/or nanoLC‐ESI‐LIT‐MS/MS, probably as a result of the poor information available on L. culinaris genome. A comparison of these maps revealed that 103 protein spots were differentially expressed within and between populations. The multivariate statistical analyses carried out on these variably expressed spots showed that 24 protein species were essential for population discrimination, thus determining their proposition as landrace markers. Besides providing the first reference map of mature lentil seeds, our data confirm previous studies based on morphological/genetic observations and further support the valuable use of proteomic techniques as phylogenetic tool in plant studies.     

The genesis and early developments of Aitken’s process,Shanks’ transformation,the ε–algorithm,and related fixed point methods

Numerical Algorithms - In this paper, we trace back the genesis of Aitken’s Δ2 process and Shanks’ sequence transformation. These methods, which are extrapolation methods, are used...     

Mass spectrometric analysis reveals O-methylation of pyruvate kinase from pancreatic cancer cells

Pyruvate kinase (PK) is an important glycolytic enzyme that catalyzes the dephosphorylation of phosphoenolpyruvate to pyruvate. Human PK isozyme M2 (PKM2), a splice variant of M1, is overexpressed in many cancer cells, and PKM2 has been investigated as a potential tumor marker for diagnostic assays and as a target for cancer therapy. To facilitate identification and characterization of PK, we studied the enzyme from pancreatic cancer cells and normal pancreatic duct cells by electrophoresis and mass spectrometry, and identified multiple O-methylated residues from PK. These findings advance our knowledge of the biochemical properties of PK and will be important in understanding its biological function in cells.

Intra-Laboratory Validation of Alpha-Galactosidase Activity Measurement in Dietary Supplements

Introduction: Alpha-galactosidase (α-Gal) is an enzyme responsible for the hydrolyzation of glycolipids and glycoprotein commonly found in dietary sources. More than 20% of the general population suffers from abdominal pain or discomfort caused by intestinal gas and by indigested or partially digested food residuals. Therefore, α-Gal is used in dietary supplements to reduce intestinal gases and help complex food digestion. Marketed enzyme-containing dietary supplements must be produced in accordance with the Food and Drug Administration (FDA) regulations for Current Good Manufacturing Practice (cGMPs). Aim: in this work we illustrated the process used to develop and validate a spectrophotometric enzymatic assay for α-Gal activity quantification in dietary supplements. Methods: The validation workflow included an initial statistical-phase optimization of materials, reagents, and conditions, and subsequently a comparative study with another fluorimetric assay. A final validation of method performance in terms of specificity, linearity, accuracy, intermediate-precision repeatability, and system precision was then executed. Results and conclusions: The proven method achieved good performance in the quantitative determination of α-Gal activity in commercial food supplements in accordance with the International Council for Harmonisation of Technical Requirements for Pharmaceuticals (ICH) guidelines and is suitable as a rapid in-house quality control test.