To exist or not to exist: example generation in Real Analysis

This article deals with the activity of example generation as a special case of problem solving. We asked university students in the scientific-technological area to produce examples (which may exist or not) of mathematical objects fulfilling given requirements. For the analysis of students’ performances, we have developed a model that attempts to grasp the nature of the different stages in the solving process. The discussion of the findings allows us to outline specificities and educational potentialities of example generation activities.     

On reduced complexity of closed piecewise linear 5-manifolds

Periodica Mathematica Hungarica - The goal of this paper is to give some theorems which relate to the problem of classifying combinatorial (resp. smooth) closed 5-manifolds up to piecewise-linear...     

Activation measurement of the 3He(alpha,gamma)7Be cross section at low energy

The nuclear physics input from the 3He(alpha,gamma)7Be cross section is a major uncertainty in the fluxes of 7Be and 8B neutrinos from the Sun predicted by solar models and in the 7Li abundance obtained in big-bang nucleosynthesis calculations. The present work reports on a new precision experiment using the activation technique at energies directly relevant to big-bang nucleosynthesis. Previously such low energies had been reached experimentally only by the prompt-gamma technique and with inferior precision. Using a windowless gas target, high beam intensity, and low background gamma-counting facilities, the 3He(alpha,gamma)7Be cross section has been determined at 127, 148, and 169 keV center-of-mass energy with a total uncertainty of 4%. The sources of systematic uncertainty are discussed in detail. The present data can be used in big-bang nucleosynthesis calculations and to constrain the extrapolation of the 3He(alpha,gamma)7Be astrophysical S factor to solar energies.     

On the computation of l- groups and natural maps

In this paper we compute surgery (resp. splitting) obstruction groups, here calledL-groups, and natural maps for many diagrams of oriented finite (not necessary abelian) 2-groups and homomorphisms which preserve orientations.     

Theoretical study of metiamide,a histamine H2 antagonist

The requirements for H₂-antagonist activity so far identified for most of the known antagonists of histamine are the presence of a heterocyclic ring containing a basic center linked via a methylene chain to a substituted guanidine or thiourea polar side chain. Metiamide is a potent H₂ antagonist (pA2=6.06). We have used the ab initio Hartree–Fock (HF) method in order to study the conformational properties of the N₃(SINGLE BOND)H tautomers of metiamide molecule and histamine monocation. Three basis set (the 3-21G*, 6-31G**, and 6-31+G**) were used, the results compared, and the geometric parameters fully optimized. Our results indicate the preference of metiamide for a folded conformation with an intramolecular hydrogen bonding between the imidazole ring and one of the NH groups. The optimized geometrical parameters and charge distributions of both molecules, using the Mulliken, and natural bond order (NBO) analysis, are given and discussed. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 117–128, 1998     

Residue analysis of glucocorticoids in bovine milk by liquid chromatography–tandem mass spectrometry

A sensitive liquid chromatography–tandem mass spectrometry (LC-MS/MS) method for the simultaneous determination of 13 steroidal anti-inflammatory drugs in bovine milk is presented. Due to their weakly acid nature, analytes were separated by ion suppression reversed phase chromatography and detected in positive-ion mode by a high flow electrospray source. Dexamethasone-d4 was used as internal standard. The sample preparation was simple and reliable; it included acidic deproteinization of milk followed by sample enrichment and clean-up, utilizing a C18 solid phase extraction cartridge. Recoveries exceeded 70% with an intra-day precision not larger than 12%. The efficiency of the sample clean-up and internal standardization rendered negligible the matrix effect, estimated by comparing standard and matrix-matched calibration curves. A small-scale reconnaissance was carried out on several raw and whole fresh milk samples. A large number of analyzed samples showed a chromatographic peak, in the retention time window of cortisol, at levels included between its decision limit (CCα) and detection capability (CCβ). As a result of a heat-induced transformation, an isomeric product of triamcinolone was observed during the extract evaporation. Since this rearrangement might occur during the milk pasteurization process, LC-MS/MS and ¹H-NMR investigations were performed out to conclusively differentiate the two isomers. One- and two-dimensional proton NMR spectra were able to identify the transformation product as 9a-fluoro-11b,16a-trihydroxy-17b-hydroxymethyl-D-homoandrosta-1,4-diene-3,17a-dione.     

An actively vetoed Clover \gamma -detector for nuclear astrophysics at LUNA

An escape-suppressed, composite high-purity germanium detector of the Clover type has been installed at the Laboratory for Underground Nuclear Astrophysics (LUNA) facility, deep underground in the Gran Sasso Laboratory, Italy. The laboratory $ \gamma$ -ray background of the Clover detector has been studied underground at LUNA and, for comparison, also in an overground laboratory. Spectra have been recorded both for the single segments and for the virtual detector formed by online addition of all four segments. The effect of the escape suppression shield has been studied as well. Despite their generally higher intrinsic background, escape-suppressed detectors are found to be well suited for underground nuclear-astrophysics studies. As an example for the advantage of using a composite detector deep underground, the weak ground-state branching of the E _p = 223 keV resonance in the ²⁴Mg(p, $ \gamma$ )²⁵Al reaction is determined with improved precision.     

Secondary school mathematics teachers and their training in pre- and post-unity Italy (1810–1920)

This paper traces the evolution of the profession of mathematics teacher in Italy during the transition of the country from a cluster of small, individual states to a single, unified nation. Our focus will be on the plans carried out for teacher training in the period from 1810, when the Scuola Normale Superiore in Pisa was created to train prospective teachers, to 1920, when the Scuole di Magistero (Teacher Training Schools) were suppressed. In particular, we have set two objectives: (a) to show how the idea changed of what disciplinary and pedagogical knowledge was useful for training future teachers, (b) to illustrate the contributions of a significant group of mathematics teachers who worked along several different lines for the improvement of education.     

S-factor of 14N(p,γ)15O at astrophysical energies⋆

The astrophysical S(E) factor of ¹⁴N(p,γ)¹⁵O has been measured for effective center-of-mass energies between E _eff = 119 and 367 keV at the LUNA facility using TiN solid targets and Ge detectors. The data are in good agreement with previous and recent work at overlapping energies. R-matrix analysis reveals that due to the complex level structure of ¹⁵O the extrapolated S(0) value is model dependent and calls for additional experimental efforts to reduce the present uncertainty in S(0) to a level of a few percent as required by astrophysical calculations.