Solving superelliptic Diophantine equations by Baker's method

We describe a method for complete solution of the superelliptic Diophantine equation ay^p=f(x). The method is based on Baker's theory of linear forms in the logarithms. The characteristic feature of our approach (as compared with the classical method) is that we reduce the equation directly to the linear forms in logarithms, without intermediate use of Thue and linear unit equations. We show that the reduction method of Baker and Davenport [3] is applicable for superelliptic equations, and develop a very efficient method for enumerating the solutions below the reduced bound. The method requires computing the algebraic data in number fields of degree pn(n-1)/2 at most; in many cases this number can be reduced. Two examples with p=3 and n=4 are given.     

Neutron scattering studies of crystal structure and crystalline electric field in high-Tc ErBa2Cu3Ox disordered by fast neutron irradiation

The crystal structure and the crystalline-electric-field splitting of the Er³⁺ 4f-shell in the high-T_c superconductor ErBa₂Cu₃O_x (x = 6.95, 6.18) disordered with fast neutron irradiation has been investigated by elastic and inelastic neutron scattering techniques, respectively. The results yield evidence for the absence of a charge transfer between the planes and chains under disorder and point to the atomic displacements being the main radiation-induced defects in the CuO₂ planes.     

Facile functionalization of a fully fluorescent perfluorophenyl BODIPY: photostable thiol and amine conjugates

Selective nucleophilic substitution on a perfluorophenyl unit comprising a BODIPY fluorophore using an alkanethiol or a primary amine offers a quantitative fluorophore labelling strategy, while retaining high photostability and emission quantum yields approaching unity.     

Design, Modeling, Fabrication, and Evaluation of the Air Amplifier for Improved Detection of Biomolecules by Electrospray Ionization Mass Spectrometry

Through a multi-disciplinary approach, the air amplifier is being evolved as a highly engineered device to improve detection limits of biomolecules when using electrospray ionization. Several key aspects have driven the modifications to the device through experimentation and simulations. We have developed a computer simulation that accurately portrays actual conditions and the results from these simulations are corroborated by the experimental data. These computer simulations can be used to predict outcomes from future designs resulting in a design process that is efficient in terms of financial cost and time. We have fabricated a new device with annular gap control over a range of 50 to 70 μm using piezoelectric actuators. This has enabled us to obtain better aerodynamic performance when compared to the previous design (2× more vacuum) and also more reproducible results. This is allowing us to study a broader experimental space than the previous design which is critical in guiding future directions. This work also presents and explains the principles behind a fractional factorial design of experiments methodology for testing a large number of experimental parameters in an orderly and efficient manner to understand and optimize the critical parameters that lead to obtain improved detection limits while minimizing the number of experiments performed. Preliminary results showed that several folds of improvements could be obtained for certain condition of operations (up to 34 folds).     

Doubly-charged ions in the planetary ionospheres: a review

This paper presents a review of the current knowledge on the doubly-charged atomic and molecular positive ions in the planetary atmospheres of the Solar System. It is focused on the terrestrial planets which have a dense atmosphere of N(2) or CO(2), i.e. Venus, the Earth and Mars, but also includes Titan, the largest satellite of Saturn, which has a dense atmosphere composed mainly of N(2) and a few percent of methane. Given the composition of these neutral atmospheres, the following species are considered: C(++), N(++), O(++), CH(4)(++), CO(++), N(2)(++), NO(++), O(2)(++), Ar(++) and CO(2)(++). We first discuss the status of their detection in the atmospheres of planets. Then, we provide a comprehensive review of their complex and original photochemistry, production and loss processes. Synthesis tables are provided for those ions, while a discussion on individual species is also provided. Methods for detecting doubly-charged ions in planetary atmospheres are presented, namely with mass-spectrometry, remote sensing and fine plasma density measurements. A section covers some original applications, like the possible effect of the presence of doubly-charged ions on the escape of an atmosphere, which is a key topic of ongoing planetary exploration, related to the evolution of a planet. The results of models, displayed in a comparative way for Venus, Earth, Mars and Titan, are discussed, as they can predict the presence of doubly-charged ions and will certainly trigger new investigations. Finally we give our view concerning next steps, challenges and needs for future studies, hoping that new scientific results will be achieved in the coming years and feed the necessary interdisciplinary exchanges amongst different scientific communities.     

The electrostatic probe: a tool for the investigation of the Aβ(1-16) peptide deformations using the static modes

We investigate the conformational changes of the Amyloid β(1-16) peptide induced by moving Zn(2+) ions in the solvent, which we call the electrostatic probe. We use our recently developed approach of static modes which allows treating the flexibility of biological molecules at the atomic scale. Starting from an experimental apostructure, we find that several ion impacts allow the transition of the peptide toward its folded conformation, observed experimentally in the presence of Zn(2+) ions. This result shows the ability of our model and its associated software tool to describe properly the conformational changes and opens a new path toward the molecule/molecule docking problem.     

Synthesis and reactivity of highly nucleophilic pyridines

3,4,5-Triamino-substituted pyridines are avid for electrophiles but are still willing to give them back. In these compounds three amino groups conjoin their forces into the heterocyclic nitrogen, making it a powerful Lewis base. A short and efficient synthesis is described, and the origin of its unique activity in nucleophilic organocatalysis is rationalized by kinetics and thermodynamic quantifications.