Une Conjecture de Lebesgue

Let A > 0 be an integer. The equation x⁵–y⁵ = Az⁵ wasfirst studied by Dirichlet and Lebesgue. Lebesgue conjecturedin 1843 that if A has no prime divisors of the form 10k+1, theequation has no solutions except the visible ones. Partial resultswere obtained by Lebesgue and by Terjanian in 1987. The purposeof the paper is to prove Lebesgue's conjecture. The main toolused is the method known as the elliptic Chabauty method.     

Discrete entanglement distribution with squeezed light

We show how one can entangle distant atoms by using squeezed light. Entanglement is obtained in steady state, and can be increased by manipulating the atoms locally. We study the effects of imperfections, and show how to scale up the scheme to build a quantum network.     

At-sea measurements of sound penetration into sediments using a buried vertical synthetic array

Acoustic bottom penetration experiments were carried out in a medium-grain sandy bottom at a site in St. Andrews Bay, Florida. These investigations used a new buried, vertical, one-dimensional synthetic array system where a small hydrophone was water-jetted into the sediment to a depth of approximately 2 m. Once buried, this hydrophone was mounted to a vertical robotics stage that translated the hydrophone upward in 1-cm increments. A broadband (3 to 80 kHz) spherical source, positioned 50 cm above the sediment-water interface, was used to insonify the sediment. Measurements were made with insonification angles above and below the critical angle by changing the horizontal distance of the source relative to the insertion point. This new measurement system is detailed, and results are presented that include temporal, frequency, and wavenumber analysis for natural and roughened interfaces. The measured compressional sound speed and attenuation are shown to be self-consistent using the Kramers-Kronig relation. Furthermore, only a single fast compressional wave was observed. There was no observation of a second slower compressional wave as predicted by some applications of the Biot model to unconsolidated water-saturated porous media.     

Synthesis of N-(2-methylpropyl)-2E-undecene-8,10-diynamide, a novel constituent of Echinacea angustifolia

The first synthesis of a diacetylenic amide from Echinacea is reported. The key steps included the reaction of an aldehyde with the monoanion of a diacetylene and the reductive removal of a propargylic alcohol.     

New beta-strand macrocyclic peptidomimetic analogues containing alpha-(O-, S- or NH-)aryl substituted glycine residues: synthesis,chemical and enzymatic properties

In so much as bis-macrocyclic peptidomimetics have been recognized as high affinity substrates for HIV-1 protease, we were interested in the design and synthesis of new bis-macrocyclic bioisosteric analogues whose general structure is displayed on Fig. 2. The structures of these new analogues are characterized by the specific replacement of the methylene of the benzyl group directly attached to the N-acyl glycine residue in the original molecule 1, by its main bioisosteres, i.e. O-, S- and NH-aryl groups. Knowing that an intermediate in which an heteroatomic aryl group is directly linked to a free amine glycine residue is not stable, we developed an original synthetic pathway which involved the coupling of a specific side chain to the exocyclic carboxylic acid function, followed by an elegant oxidation-nucleophilic substitution Steglich-type reaction. Analogues 2a-d were then submitted to chemical and enzymatic hydrolysis. We demonstrated that, as expected, the specific cleavage of the exocyclic N-acyl bond led to the release of aryl moieties (phenol, thiophenol and aniline species). These chemical and enzymatic stability studies brought to light the biological potential of such macrocyclic analogues in infected cells.     

Antifeedant activity of some Sri Lankan plants

Twenty nine solvent extracts from twenty Sri Lankan plants were examined for antifeedant activity against the fourth instar larvae of Mexican bean beetle, Epilachna varivestis Muls., Coccinellidae. Extracts of Sarcococca brevifolia (Buxaceae), Strychnus nux vomica (Loganiaceae), Diploclisia glaucescens, Coscinium fenestratum (Menispermaceae), Syzygium caryophyllatum (Myrtaceae), Pittosporium zeylanicum (Pittosporaceae), Lasianthus gardneri (Rubiaceae), Ferronia limonia (Rutaceae) and Allophylus cobbe (Sapindaceae) have shown strong antifeedant activity.     

Synthetic approach to malibatol A

[reaction: see text] A synthetic approach to malibatol A featuring a novel benzofuran synthesis is described.     

Observation of bi-polarons in blends of conjugated copolymers and fullerene derivatives

From a fundamental and application point of view it is of importance to understand how charge carrier generation and transport in a conjugated polymer (CP):fullerene blend are affected by the blend morphology. In this work light-induced electron spin resonance (LESR) spectra and transient ESR response signals are recorded on non-annealed and annealed blend layers consisting of alkyl substituted thieno[3,2-b]thiophene copolymers (pATBT) and the soluble fullerene derivative [6,6]-phenyl-C61-butyric acid methyl ester (PCBM) at temperatures ranging from 10 to 180 K. Annealing of the blend sample leads to a reduction of the steady state concentration of light-induced PCBM anions within the blend at low temperatures (T = 10 K) and continuous illumination. This is explained on the basis of the reducing interfacial area of the blend composite on annealing, and the high activation energy for electron diffusion in PCBM blends leading to trapped electrons near the interface with the CP. As a consequence, these trapped electrons block consecutive electron transfer from an exciton on a CP to the PCBM domain, resulting in a relatively low concentration charge carriers in the annealed blend. Analysis of the transient ESR data allows us to conclude that in annealed samples diamagnetic bi-polaronic states on the CPs are generated at low temperature. The formation of these states is related to the generation and interaction of multiple positive polarons in the large crystalline polymer domains present in the annealed sample.