Since their appearance new technologies have raised many expectations about their potential for innovating teaching and learning practices; in particular any didactical software, such as a Dynamic Geometry System (DGS) or a Computer Algebra System (CAS), has been considered an innovative element suited to enhance mathematical learning and support teachers’ classroom practice. This paper shows how the teacher can exploit the potential of a DGS to overcome crucial difficulties in moving from an intuitive to a deductive approach to geometry. A specific intervention will be presented and discussed through examples drawn from a long-term teaching experiment carried out in the 9th and 10th grades of a scientific high school. Focusing on an episode through the lens of a semiotic analysis we will see how the teacher’s intervention develops, exploiting the semiotic potential offered by the DGS Cabri-Géomètre. The semiotic lens highlights specific patterns in the teacher’s action that make students’ personal meanings evolve towards the mathematical meanings that are the objective of the intervention. 相似文献
The combined use of the Sharpless asymmetric epoxidation, a number of stereospecific chemical transformations, and the 3,5-hexadienoic acid benzannulation protocol allowed us to devise a new, divergent, and stereoselective approach to terpenes with a chiral tertiary hydroxyl group at the ortho-position of a phenol functional group. Accordingly, the natural occurring enantiomeric forms of the bisabolane sesquiterpenes (+)-curcutetraol, (+)-sydonol, (+)-sydonic acid, and (+)-7-O-methylsydonic acid were synthesized with high enantiomeric purity starting from geraniol. The latter two acids were prepared in enantioenriched form for the first time. 相似文献
Shape from shading (SFS) denotes the problem of reconstructing a 3D surface, starting from a single shaded image which represents the surface itself. Minimization techniques are commonly used for solving the SFS problem, where the objective function is a weighted combination of the brightness error, plus one or more terms aiming to obtain a valid solution. We present a regularized quadratic penalty method where quadratic penalization is used to adaptively adjust the smoothing weights, and regularization improves the robustness and reliability of the procedure. A nonmonotone Barzilai–Borwein method is employed to efficiently solve the arising subproblems. Numerical results are provided showing the reliability of the proposed approach. 相似文献
Mass spectrometry imaging with desorption electrospray ionization mass spectrometry (DESI-MS) is used to characterize cancer from ex vivo slices of tissues. The process is time-consuming. The use of tissue smears for DESI-MS analysis has been proposed as it eliminates the time required to snap-freeze and section the tissue. To assess the utility of tissue smears for rapid cancer characterization, principal component analysis (PCA) was performed to evaluate the concordance between DESI-MS profiles of breast cancer from tissue slices and smears prepared on various surfaces. PCA suggested no statistical discrimination between DESI-MS profiles of tissue sections and tissue smears prepared on glass, polytetrafluoroethylene (PTFE), and porous PTFE. However, the abundances of cancer biomarker ions varied between sections and smears, with DESI-MS analysis of tissue sections yielding higher ion abundances of cancer biomarkers compared with smears. Coefficient of variance (CV) analysis suggests DESI-MS profiles from tissue smears are as reproducible as the ones from tissue sections. The limit of detection with smear samples from single pixel analysis is comparable to tissue sections that average the signal from a tissue area of 0.01 mm2. The smears prepared on the PTFE surface possessed a higher degree of homogeneity compared with the smears prepared on the glass surface. This allowed single MS scans (~1 s) from random positions across the surface of the smear to be used in rapid cancer typing with good reproducibility, providing pathologic information for cancer typing at speeds suitable for clinical utility.