Singular Hamiltonian elliptic systems with critical exponential growth in dimension two

We will focus on the existence of nontrivial solutions to the following Hamiltonian elliptic system where are numbers belonging to the interval [0, 2), V is a continuous potential bounded below on by a positive constant and the functions f and g possess exponential growth range established by Trudinger–Moser inequalities in Lorentz–Sobolev spaces. The proof involves linking theorem and a finite‐dimensional approximation.     

Fluorine in Small Molecules: Fluoromethyl Azide and Chalcogenocyanates

Fluoromethylating agents are a highly studied and controversely discussed class of compounds. New fluoromethyl pseudohalides FCH₂N₃, FCH₂SCN, and FCH₂SeCN were prepared for the first time and their physical and spectroscopic properties investigated. Their synthesis is performed conveniently by fluoromethylation of the respective silver or potassium pseudohalogenides with fluoroiodomethane.     

Existence and concentration of solutions for a class of biharmonic equations

Some superlinear fourth order elliptic equations are considered. A family of solutions is proved to exist and to concentrate at a point in the limit. The proof relies on variational methods and makes use of a weak version of the Ambrosetti–Rabinowitz condition. The existence and concentration of solutions are related to a suitable truncated equation.     

Optimization and validation of organochlorine compounds in adipose tissue by SPE‐gas chromatography

Scientific evidence has shown an association between organochlorine compounds (OCC) exposure and human health hazards. Concerning this, OCC detection in human adipose samples has to be considered a public health priority. This study evaluated the efficacy of various solid‐phase extraction (SPE) and cleanup methods for OCC determination in human adipose tissue. Octadecylsilyl endcapped (C₁₈‐E), benzenesulfonic acid modified silica cation exchanger (SA), poly(styrene‐divinylbenzene (EN) and EN/RP₁₈ SPE sorbents were evaluated. The relative sample cleanup provided by these SPE columns was evaluated using gas chromatography with electron capture detection (GC–ECD). The C₁₈‐E columns with strong homogenization were found to provide the most effective cleanup, removing the greatest amount of interfering substance, and simultaneously ensuring good analyte recoveries higher than 70%. Recoveries > 70% with standard deviations (SD) < 15% were obtained for all compounds under the selected conditions. Method detection limits were in the 0.003–0.009 mg/kg range. The positive samples were confirmed by gas chromatography coupled with tandem mass spectrometry (GC‐MS/MS). The highest percentage found of the OCC in real samples corresponded to HCB, o,p′‐DDT and methoxychlor, which were detected in 80 and 95% of samples analyzed respectively. Copyright © 2012 John Wiley & Sons, Ltd.     

Laser stabilization to an atomic transition using an optically generated dispersive line shape

We report a simple and robust technique to generate a dispersive signal which serves as an error signal to electronically stabilize a monomode continuous-wave laser emitting around an atomic resonance. We explore nonlinear effects in the laser beam propagation through a resonant vapor by way of spatial filtering. The performance of this technique is validated by locking semiconductor lasers to the cesium and rubidium D₂ lines and observing long-term reduction of the emission frequency drifts, making the lasers well adapted for many atomic physics applications.     

Exact pressure integrations on submerged bodies in waves using a quadtree adaptive mesh algorithm

The development of an adaptive free surface, mesh cutting, methodology, in order to analytically integrate pressures on varying wet parts of partially submerged surfaces in the presence of waves, is presented. Given a function of free‐surface elevation, the algorithm checks for the intersection of the body with the free surface and, based on user‐defined parameters, modifies the initial mesh, by subdividing the elements where necessary and eliminating others, via a quadtree approach. Redundant sub‐divisions, generated in the quad‐division process, are partially eliminated, but the quadrilateral nature of the elements is always kept. The free‐surface function must be single‐valued and its definition domain simply connected. Hydrostatic and Froude–Krylov forces are computed exactly on each panel by means of analytical formulations, which are derived and presented, based on the theory of linear gravity waves and from applying Green's theorem. Copyright © 2014 John Wiley & Sons, Ltd.     

Dynamics of Robertson–Walker spacetimes with diffusion

We study the dynamics of spatially homogeneous and isotropic spacetimes containing a fluid undergoing microscopic velocity diffusion in a cosmological scalar field. After deriving a few exact solutions of the equations, we continue by analyzing the qualitative behavior of general solutions. To this purpose we recast the equations in the form of a two dimensional dynamical system and perform a global analysis of the flow. Among the admissible behaviors, we find solutions that are asymptotically de-Sitter both in the past and future time directions and which undergo accelerated expansion at all times.