Computing the conjugate of convex piecewise linear-quadratic bivariate functions

We present a new algorithm to compute the Legendre–Fenchel conjugate of convex piecewise linear-quadratic (PLQ) bivariate functions. The algorithm stores a function using a (primal) planar arrangement. It then computes the (dual) arrangement associated with the conjugate by looping through vertices, edges, and faces in the primal arrangement and building associated dual vertices, edges, and faces. Using optimal computational geometry data structures, the algorithm has a linear time worst-case complexity. We present the algorithm, and illustrate it with numerical examples. We proceed to build a toolbox for convex bivariate PLQ functions by implementing the addition, and scalar multiplication operations. Finally, we compose these operators to compute classical convex analysis operators such as the Moreau envelope, and the proximal average.     

Optimization of Schwarz waveform relaxation over short time windows

Schwarz waveform relaxation algorithms (SWR) are naturally parallel solvers for evolution partial differential equations. They are based on a decomposition of the spatial domain into subdomains, and a partition of the time interval of interest into time windows. On each time window, an iteration, during which subproblems are solved in space-time subdomains, is then used to obtain better and better approximations of the overall solution. The information exchange between subdomains in space-time is performed through classical or optimized transmission conditions (TCs). We analyze in this paper the optimization problem when the time windows are short. We use as our model problem the optimized SWR algorithm with Robin TCs applied to the heat equation. After a general convergence analysis using energy estimates, we prove that in one spatial dimension, the optimized Robin parameter scales like the inverse of the length of the time window, which is fundamentally different from the known scaling on general bounded time windows, which is like the inverse of the square root of the time window length. We illustrate our analysis with a numerical experiment.     

Feasibility of using ultrasound contrast agents to increase the size of thermal lesions induced by non-focused transducers: in vitro demonstration in tissue mimicking phantom

Miniature flat ultrasound transducers have shown to be effective for a large variety of thermal therapies, but the associated superficial heating implicates developing original strategies in order to extend therapeutic depth. The goal of the present paper is to use ultrasound contrast agents (UCA) to increase remote attenuation and heating. Theoretical simulations demonstrated that increasing attenuation from 0.27 to 0.8 Np/cm at 10 MHz beyond a distance of 18 mm from the transducer should result in longer thermal damages due to protein coagulation in a tissue mimicking phantom. Contrast agents (BR14, Bracco, Plan-les-Ouates, Switzerland) were embedded in thermo-sensitive gel and attenuations ranging from 0.27 to 1.33 Np/cm were measured at 10 MHz for concentrations of BR14 between 0 and 4.8%. Thermal damages were then induced in several gels, which had different layering configurations. Thermal damages, 12.8 mm in length, were obtained in homogeneous gels. When mixing contrast agents at a concentration of 3.2% beyond a first 18 mm-thick layer of homogeneous gel, the thermal damages reached 21.5 mm in length. This work demonstrated that contrast agents can be used for increasing attenuation remotely and extending therapeutic depth induced by a non-focused transducer. Additional work must be done in vivo in order to verify the remote-only distribution of bubbles and associated increase in attenuation.     

Strongly Bounded Groups and Infinite Powers of Finite Groups

We define a group as strongly bounded if every isometric action on a metric space has bounded orbits. This latter property is equivalent to the so-called uncountable strong cofinality, recently initiated by Bergman.

Our main result is that G ^I is strongly bounded when G is a finite, perfect group and I is any set. This strengthens a result of Koppelberg and Tits. We also prove that ω₁-existentially closed groups are strongly bounded.     

Mobilité conformationnelle et migration des liaisons π dans le [24]annulène

Conformational Mobility and Migration of the π Bonds of the [24]annulene. The configuration and the conformation of [24]annulene have been determined after a detailed analysis of its ¹H-NMR spectrum recorded at −95°. At this temperature, molecular dynamics is practically frozen, and the spectrum can be correctly simulated considering eight magnetic sites with the relevant couplings. The [24]annulene exhibits alternation of the double and the single bonds with the CTTTCTTTCTTT sequence (C=cis, T=trans) expressing the connectivity of the double bonds. The signal of the 9 protons pointing inside the ring is 7.72 ppm at lower field than the signal of the 15 outer protons; this indicates a marked paramagnetic ring current. Molecular dynamics is revealed by the dependence of the spectrum upon the temperature; the simulation of the line shape of these spectra indicates that the [24]annulene in solution exists as an equilibrium of two conformers A and B ( B / A ≤0.05), both having the same configuration. Each of these conformers undergoes two isodynamic processes: a migration of the π bonds on the adjacent single bonds (bond shift) described by V and a conformational mobility described by K. The two conformers interconvert extremely rapidely. Conformer A complies with C_3h symmetry, conformer B with C₃ symmetry. The enthalpy, entropy, and free energy of activation for the processes described by V and K in the major conformer A have been determined: these processes are slower than those observed in [16]annulene. From their values, we could deduce that the resonance energy in the [24]-7³annulene is negative and of the order of −9 to −10 kcal⋅mol⁻¹.     

Speciation of major arsenic species in seawater by flow injection hydride generation atomic absorption spectrometry

Arsenic present at 1 μg L^–1 concentrations in seawater can exist as the following species: As(III), As(V), monomethylarsenic, dimethylarsenic and unknown organic compounds. The potential of the continuous flow injection hydride generation technique coupled to atomic absorption spectrometry (AAS) was investigated for the speciation of these major arsenic species in seawater. Two different techniques were used. After hydride generation and collection in a graphite tube coated with iridium, arsenic was determined by AAS. By selecting different experimental hydride generation conditions, it was possible to determine As(III), total arsenic, hydride reactive arsenic and by difference non-hydride reactive arsenic. On the other hand, by cryogenically trapping hydride reactive species on a chromatographic phase, followed by their sequential release and AAS in a heated quartz cell, inorganic As, MMA and DMA could be determined. By combining these two techniques, an experimental protocol for the speciation of As(III), As(V), MMA, DMA and non-hydride reactive arsenic species in seawater was proposed. The method was applied to seawater sampled at a Mediterranean site and at an Atlantic coastal site. Evidence for the biotransformation of arsenic in seawater was clearly shown.     

Testimony of the Correlation Between the Reactive Histidine Residue and the Arginase Catalytic Mechanism Using a Biochromatographic Concept and Mutagenesis Experiments

In a previous paper (Bagnost et al., J Chromatogr B Analyt Technol Biomed Life Sci 853:38–46, 2007), an arginase chromatographic support was developed to study the association mechanism of arginase (an enzyme which can reduce endothelial dysfunction and blood pressure rising in spontaneously hypertensive rats) with nor-NOHA a potential inhibitor of its activity. In this report mutagenesis experiments associated with this biochromatographic approach confirmed that the active-site residue Hist 141 is protonated as imidazolium cation. Hist 141 could function as a general acid to protonate the leaving amino group of l-ornithine during catalysis.     

Structural and luminescent properties of micro- and nanosized particles of lanthanide terephthalate coordination polymers

Reaction in water between rare earth ions (Ln = Y, La-Tm, except Pm) and the sodium salt of terephthalic acid leads to a family of lanthanide-based coordination polymers of general formula [Ln2(C8H4O4)3(H2O)4] n with Ln = La-Tm or Y. The isostructurality of the compounds with the previously reported Tb-containing polymer is ascertained on the basis of their X-ray powder diffraction diagrams. The coordination water molecules can be reversibly removed without destroying the crystal structure for compounds involving one of the lighter lanthanide ions (La-Eu). For compounds involving one of the heavier lanthanide ions (Tb-Tm) or yttrium, a structural change occurs during the drying process. X-ray diffraction data show this new anhydrous phase corresponding to the linking of pairs of Er(III) ions through mu-carboxylate bridges. Porosity profiles calculated for the anhydrous phases of Tb(III) and Er(III) show the presence of channels with very small sections. The luminescent properties of all the compounds have been recorded and the two most luminescent polymers, namely, the europium- and the terbium-containing ones, have been studied in more detail. Tb(III)-containing compounds display large quantum yields, up to 43%. Polyvinylpyrrolidone nanoparticles doped with [Ln2(C8H4O4)3(H2O)4] n (Ln = Eu, Tb, Er) have also been synthesized and characterized. The encapsulation of the coordination polymers results in somewhat reduced luminescence intensities and lifetime, but the nanoparticles can be dispersed in water and remain unchanged in this medium for more than 20 h.