CE‐ESI‐TOF/MS for human growth hormone analysis

CE is a powerful analytical tool used to separate intact biomolecules such as proteins. The coupling of CE with TOF/MS produces a very promising method that can be used to detect and identify proteins in different matrices. This paper describes an efficient, rapid, and simple CE‐ESI‐TOF/MS procedure for the analysis of endogenous human growth hormone and recombinant human growth hormone without sample preparation. Operational factors were optimized using an experimental design, and the method was successfully applied to distinguish human growth hormone and recombinant human growth hormone in unknown samples.     

Mathematics teacher education advanced methods: an example in dynamic geometry

We present a research work about an innovative national teacher training program in France: the Pairform@nce program, designed to sustain ICT integration. We study here training for secondary school teachers, whose objective is to foster the development of an inquiry-based approach in the teaching of mathematics, using investigative potentialities of dynamic geometry environments. We adopt the theoretical background of the documentational approach to didactics. We focus on the interactions between teachers and resources: teachers’ professional knowledge influences these interactions, which at the same time yield knowledge evolutions, a twofold process that we conceptualise as a documentational genesis. We followed in particular the work of a team of trainees; drawing on the data collected, we analyse their professional development, related with the training. We observe intertwined evolutions and stabilities, consistent with ongoing geneses.     

Fast and accurate algorithm for the simulation of NMR spectra of large spin systems

The computational cost for the simulation of NMR spectra grows exponentially with the number of nuclei. Today, the memory available to store the Hamiltonian limits the size of the system that can be studied. Modern computers enable to tackle systems containing up to 13 spins [1], which obviously does not allow to study most molecules of interest in research. This issue can be addressed by identifying groups of spins or fragments that are not or only weakly interacting together, i.e., that only share weakly coupled spin pairs. Such a fragmentation is only permitted in the weak coupling regime, i.e., when the coupling interaction is weak compared to the difference in chemical shift of the coupled spins. Here, we propose a procedure that removes weak coupling interactions in order to split the spin system efficiently and to correct a posteriori for the effect of the neglected couplings. This approach yields accurate spectra when the adequate interactions are removed, i.e., between spins only involved in weak coupling interactions, but fails otherwise. As a result, the computational time for the simulation of 1D spectra grows linearly with the size of the spin system.     

Deformable two-dimensional photonic crystal slab for cavity optomechanics

We have designed photonic crystal suspended membranes with optimized optical and mechanical properties for cavity optomechanics. Such resonators sustain vibration modes in the megahertz range with quality factors of a few thousand. Thanks to a two-dimensional square lattice of holes, their reflectivity at normal incidence at 1064?nm reaches values as high as 95%. These two features, combined with the very low mass of the membrane, open the way to the use of such periodic structures as deformable end mirrors in Fabry-Perot cavities for the investigation of cavity optomechanical effects.     

A variance-based method to rank input variables of the Mesh Adaptive Direct Search algorithm

The Mesh Adaptive Direct Search algorithm (Mads) algorithm is designed for nonsmooth blackbox optimization problems in which the evaluation of the functions defining the problems are expensive to compute. The Mads algorithm is not designed for problems with a large number of variables. The present paper uses a statistical tool based on variance decomposition to rank the relative importance of the variables. This statistical method is then coupled with the Mads algorithm so that the optimization is performed either in the entire space of variables or in subspaces associated with statistically important variables. The resulting algorithm is called Stats-Mads and is tested on bound constrained test problems having up to 500 variables. The numerical results show a significant improvement in the objective function value after a fixed budget of function evaluations.     

Dimerisation Process of Silybin‐Type Flavonolignans: Insights from Theory

Natural polyphenols are known to be oxidized by free radicals, which partially explains the antioxidant properties of a number of these compounds. This oxidation may also be used to synthesise new compounds of biological interest, for example, dimers. The present theoretical study describes the existing experimental evidence showing that silybin and dehydrosilybin [natural polyphenols isolated from milk thistle (Silybum marianum)] form dimers regioselectively. Based on DFT calculations, thermodynamic and kinetic values were computed in order to better understand the physicochemical behaviour of these dimerisation processes. Calculations showed that after H‐atom transfer (from polyphenol to radical), dimerisation could proceed in two steps: 1) bond formation and, when possible, 2) tautomerisation reorganisation. The former step is the limiting step, while the latter is crucial for the process to be thermodynamically favourable (ΔG<0). If this rearrangement is impossible then dimerisation is not feasible, or at least becomes a minor process (e.g., dehydrosilybin dimerisation after H‐atom abstraction from the 3‐OH group). This explains the regioselectivity of polyphenol dimerisation.     

Surface modification of an epoxy resin with polyamines via cyanuric chloride coupling

The presence of polyamine groups on the surface of dielectric resins potentially improves the adhesion with electrochemically deposited metals. In this article, first cyanuric chloride is covalently bound to the surface hydroxyl groups of the epoxy resin. The remaining reactive sites on the coupled cyanuric chloride molecule are then used to anchor polyamines. New data on the triazine coupling is presented. The surface reactions are monitored and characterized by means of ATR-IR, SEM-EDS, XPS and ToF-S-SIMS.     

Nonsmooth Calculus, Minimality, and Monotonicity of Convexificators

Noncompact convexificators, which provide upper convex and lower concave approximations for a continuous function, are defined. Various calculus rules, including extremality and mean-value properties, are presented. Regularity conditions are given for convexificators to be minimal. A characterization of quasiconvexity of a continuous function is obtained in terms of the quasimonotonicity of convexificators.     

Pseudovaluation domains with vapnik-chervonenkis classes of definable sets

We use model-theoretic methods to give examples of pseudovaluation domains with Vapnik-Chervonenkis classes of definable sets.