Idempotent measures on locally compact semigroups

Summary The structure of the support F of an idempotent probability measure on a locally compact semigroup S is considered. It is shown that if S satisfies the condition (L): AB ^–1 is compact whenever A and B are compact subsets of S, then F is a completely simple semigroup and has the canonical representation X ×G×Y of which G and Y are compact. Moreover, is a product measure _X × _G × _Y where _X and _Y are probability measures and _G is the Haar measure on the group G. We conjecture that a similar result remains true even without the condition (L). We give also a relation between our conjecture and a conjecture of Argabright on the support of an r ^*-invariant measure.     

Géométrie de la chaînette ou hypergéométrie

Summary Differential calculus is proving inefficient to solve problems of mechanics dealing with ropes, unless one satisfies oneself with rough approximations.Ordinary or Euclidean geometry is also proving useless: The author shows that in order to solve such problems as described before, one has to use a special branch of geometry. Distances are no longer measured along rigid straight rules, but along the catenary curves in question.The fundamental characteristics of this hypergeometry, with some of their more striking results, are described in the following study.     

Constitutional dynamic self-sensing in a zinc(II)/polyiminofluorenes system

The interaction of an external effector, ZnII ions, with a constitutional dynamic library of fluorescent polyiminofluorenes leads to component exchange, which generates an entity responding by a change in emission to the effector that has induced its formation. The overall coupled system displays a tuning of optical signal, resulting from two synergistic processes: adaptative constitutional reorganization and self-sensing. In broader terms, this work highlights the perspectives opened by constitutional dynamic chemistry toward the design of smart materials, capable of expressing different latent properties in response to environmental conditions.     

Engineering of highly luminescent lanthanide tags suitable for protein labeling and time-resolved luminescence imaging

The synthesis of a new ligand LH(4) based on a glutamic acid skeleton bis-functionalized on its nitrogen atom by 6-methylene-6'-carboxy-2,2'-bipyridine chromophoric units is described. UV-vis spectrophotometric titrations revealed the formation of 1:1 M:L complexes with lanthanide(III) cations, and complexation of LH(4) with equimolar amounts of hydrated LnCl(3) salts (Ln = Eu, Gd, and Tb) gave water-soluble and stable complexes of the general formula [LnL(H(2)O)]Na, which were characterized by elemental analysis, IR, UV-vis absorption spectroscopy, (1)H NMR (Ln = Eu), and mass spectrometry. The conditional stability constant for formation of the [EuL(H(2)O)]Na complex was determined by competitive complexation experiments to be log K = 16.5 +/- 0.6 in 0.01 M TRIS/HCl buffer (pH = 7.0). In water solution, the [EuL(H(2)O)]Na and [TbL(H(2)O)]Na complexes were highly luminescent with quantum yields of 8% and 31%, respectively, despite the presence of ca. one water molecule in the first coordination sphere of the metal ions. Activation of the appended carboxylate function of the glutamate moiety in the form of an N-hydroxysuccinimidyl ester allows for the covalent linking of the complexes to primary amino groups of biological compounds. Bovine serum albumin (BSA) was labeled with both Eu or Tb complexes, and the Ln-BSA conjugates were characterized by UV-vis absorption and emission spectroscopy and MALDI-TOF mass spectrometry. Labeling ratios (number of complex molecules per BSA) of ca. 8:1 and 7:1 were established for Eu-BSA and Tb-BSA, respectively. The suitability of the tagged compound for use in bioanalytical time-resolved luminescence microscopy was established by comparison with fluorescein-labeled probes.     

Synthesis of selenium-derivatized cytidine and oligonucleotides for X-ray crystallography using MAD

Synthesis of the novel 2'-Se-cytidine phosphoramidite was achieved via transformation of the uridine analogue to the cytidine derivative in high yield. This 2'-Se-cytidine phosphoramidite was used to synthesize selenium-derivatized DNA and RNA oligonucleotides for X-ray crystallography using MAD. The nucleotide coupling yield using this novel phosphoramidite was over 99% when 5-benzylmercaptotetrazole (5-BMT) was used as the coupling reagent.     

Enzymatic synthesis of phosphoroselenoate DNA using thymidine 5'-(alpha-P-seleno)triphosphate and DNA polymerase for X-ray crystallography via MAD

We report here the first study of enzymatic synthesis of two phosphoroselenoate (PSe) DNAs using the two alpha-Se-TTP diastereomers (Sp and Rp) and DNA polymerase. The experimental results indicate that Klenow equally recognizes the two individual diastereomers at the same level as natural TTP. The incorporations of the PSe groups at the expected sites have been confirmed by the digestion resistance to exonuclease III, and the different patterns of the digestion resistance of DNA I and II indicate the configurational differences of the PSe centers (Sp or Rp). Unlike chemical synthesis, which is limited to short DNAs and where the separation of the PSe DNA diastereomers is necessary, this enzymatic method can be used to prepare longer DNAs without diastereomer separation. This quantitative enzymatic approach is particular valuable for the synthesis of longer DNAs with multiple PSe groups in large scale for their X-ray crystal structure determination by the MAD phasing technique.     

Chemistry and biology of diazonamide A: second total synthesis and biological investigations

As an especially unique target for chemical synthesis, diazonamide A has the potential to be constructed through a plethora of synthetic routes, each attended by different challenges and opportunities for discovery. In this article, we detail our second total synthesis of diazonamide A through a sequence entirely distinct from that employed in our first campaign, one whose success required the development of several special strategies and tactics. We also disclose our complete studies regarding the chemical biology of diazonamide A and its structural congeners, and more fully delineate the scope of our protocol for Robinson-Gabriel cyclodehydration using pyridine-buffered POCl(3).     

Criteria for the approximation property for multigrid methods in nonnested spaces

We extend the abstract frameworks for the multigrid analysis for nonconforming finite elements to the case where the assumptions of the second Strang lemma are violated. The consistency error is studied in detail for finite element discretizations on domains with curved boundaries. This is applied to prove the approximation property for conforming elements, stabilized -elements, and nonconforming elements for linear elasticity on nonpolygonal domains.

     

Convergence of the Marcus–Lushnikov Process

The Smoluchowski coagulation equation describes the concentration c(t,x) of particles of mass x [ 0,] at the instant t 0, in an infinite system of coalescing particles. It is well-known that in some cases, gelation occurs: a particle with infinite mass appears. But this infinite particle is inert, in the sense that it does not interact with finite particles. We consider the so-called Marcus–Lushnikov process, which is a stochastic finite system of coalescing particles. This process is expected to converge, as the number of particles tends to infinity, to a solution of the Smoluchowski coagulation equation. We show that it actually converges, for t [0,], to a modified Smoluchowski equation, which takes into account a possible interaction between finite and infinite particles.     

Produits dans la cohomologie des variétés de Shimura : quelques calculs

We show how our recent results (arXiv: math.NT/0403407 v1 24 Mar 2004) together with a criterion of Venkataramana can be used to get explicit conditions for the virtual non-vanishing of the product of two cohomology classes of certain Shimura varieties. To cite this article: N. Bergeron, C. R. Acad. Sci. Paris, Ser. I 339 (2004).