An adaptive enrichment algorithm for advection‐dominated problems

We are interested in developing a numerical framework well suited for advection–diffusion problems when the advection part is dominant. In that case, given Dirichlet type boundary condition, it is well known that a boundary layer develops. To resolve correctly this layer, standard methods consist in increasing the mesh resolution and possibly increasing the formal accuracy of the numerical method. In this paper, we follow another path: we do not seek to increase the formal accuracy of the scheme but, by a careful choice of finite element, to lower the mesh resolution in the layer. Indeed the finite element representation we choose is locally the sum of a standard one plus an enrichment. This paper proposes such a method and with several numerical examples, we show the potential of this approach. In particular, we show that the method is not very sensitive to the choice of the enrichment and develop an adaptive algorithm to automatically choose the enrichment functions.Copyright © 2012 John Wiley & Sons, Ltd.     

C 1-generic billiard tables have a dense set of periodic points

We prove that the set of periodic points of a generic C ¹-billiard table is dense in the phase space.     

(Trifluoromethylselenyl)methylchalcogenyl as Emerging Fluorinated Groups: Synthesis under Photoredox Catalysis and Determination of the Lipophilicity

The synthesis of molecules bearing (trifluoromethylselenyl)methylchalcogenyl groups is described via an efficient two-step strategy based on a metal-free photoredox catalyzed decarboxylative trifluoromethylselenolation with good yields up to 88 %, which raised to 98 % in flow chemistry conditions. The flow methods allowed also to scale up the reaction. The mechanism of this key reaction was studied. The physicochemical characterization of these emerging groups was performed by determining their Hansch–Leo lipophilicity parameters with high values up to 2.24. This reaction was also extended to perfluoroalkylselenolation with yields up to 95 %. Finally, this method was successfully applied to the functionalization of relevant bioactive molecules such as tocopherol or estrone derivatives.     

Environmental radioactivity of soils and sediments: Egyptian sector of the Nile valley

The activity concentrations of natural ⁴⁰K, ²³²Th, and ²³⁸U in 89 soil and 84 sediment samples collected over the entire Egyptian Nile River basin including the Nile delta are reported based on the results of epithermal neutron activation analysis. The average activity concentrations of ⁴⁰K, ²³²Th, and ²³⁸U equal to 15.3?±?6.6, 15.6?±?11.1 and 220?±?31 Bq/kg, respectively, are significantly lower than those reported for the Upper Continental Crust, World Average Sediments as well as World Average Soils, suggesting the presence of a considerable portion of mafic material, most probably originating from the Ethiopian High Plateau. Their average activity concentrations are statistically the same in soil and sediments, indicating that the Nile sediments and soil material are of the same origin. The main goal of this study was not only to estimate the radiological hazards but also to show the influence of sedimentary material transportable by the Blue Nile from the Ethiopian High Plateau. The different hazard indices like the radium equivalent, gamma index, external hazard as well as the internal hazard show a low radiological exposure either on direct contact or if local mud bricks are used in the construction of dwellings.     

Phosphahelicenes with (Thio)Phosphinic Acid and Ester Functions by the Oxidative Photocyclisation Approach

Phosphahelicenes with thiophosphinic acid and ester functions have been obtained by the oxidative photocyclisation of olefins bearing both a benzophenanthrene and a benzophosphole unit. When the method has been extended to olefins bearing a partially saturated benzophospholene unit, a divergent regioselectivity of the photocyclisation step has been observed, leading to new helicenes in which the phosphorus function is located on the external rim of the helical backbone. The observed regioselectivity correlates well with the free-valence numbers of the atoms involved in the photocyclisation reaction (DFT calculations).     

A Note on Convergence of the Equi-Energy Sampler

This paper studies maximum likelihood estimation for a parameterised elliptic diffusion in a manifold. The focus is on asymptotic properties of maximum likelihood estimates obtained from continuous time observation. These are well known when the underlying manifold is a Euclidean space. However, no systematic study exists in the case of a general manifold. The starting point is to write down the likelihood function and equation. This is achieved using the tools of stochastic differential geometry. Consistency, asymptotic normality and asymptotic optimality of maximum likelihood estimates are then proved, under regularity assumptions. Numerical computation of maximum likelihood estimates is briefly discussed.     

Exciton Interactions,Excimer Formation,and [2π+2π] Photodimerization in Nonconjugated Curcuminoid-BF2 Dimers

We describe the synthesis of a series of covalently linked dimers of quadrupolar curcuminoid-BF₂ dyes and the detailed investigation of their solvent-dependent spectroscopic and photophysical properties. In solvents of low polarity, intramolecular folding induces the formation of aggregated chromophores, the UV/Vis absorption spectra of which display the optical signature characteristic of weakly-coupled H-aggregates. The extent of folding and, in turn, of ground-state aggregation is strongly dependent on the nature of the flexible linker. Steady-state and time-resolved fluorescence emission spectroscopies show that the Frenkel exciton relaxes into a fluorescent symmetrical excimer state with a long lifetime. Furthermore, our in-depth studies show that a weakly emitting excimer lies on the pathway toward a photocyclomer. Two-dimensional ¹H NMR spectroscopy and density functional theory (DFT) allowed the structure of the photoproduct to be established. To our knowledge, this represents the first example of a [2π+2π] photodimerization of the curcuminoid chromophore.     

Access to New Endoperoxide Derivatives by Electrochemical Oxidation of Substituted 3‐Azabicyclo[4.1.0]hept‐4‐enes

A series of substituted 3‐azabicyclo[4.1.0]hept‐4‐ene derivatives were prepared and analysed by cyclic voltammetry. Preparative aerobic electrochemical oxidation reactions were then carried out. Three original endoperoxides were isolated, characterised and subjected to antimalarial and cytotoxicity activity assays.