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.     

Contents of Volume 4 (2001)

Volume Contents

Contents of Volume 4 (2001)     

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.     

Oxidation of 5-hydroxy-2'-deoxyuridine into isodialuric acid, dialuric acid, and hydantoin products

Oxidation products of cytosine, including 5-hydroxycytosine and 5-hydroxyuracil, are highly susceptible to subsequent oxidation. Here, the oxidation products of 5-hydroxy-2'-deoxyuridine have been studied by NMR and MS analyses. The initial products were diastereomers of isodialuric acid nucleoside. These products subsequently decomposed into corresponding dialuric acid derivatives at neutral pH. The position of the carbonyl and hydroxyl groups, at C5 and C6 for isodialuric acid and at C6 and C5 for dialuric acid derivatives, respectively, was determined by 1H- and 13C NMR analyses. In addition, these analyses revealed that the carbonyl groups of both isodaluric and dialuric acid derivatives exist in their fully hydrated form in aqueous solution. Finally, the dialuric acid derivatives were observed to undergo subsequent decomposition into the corresponding 5-hydroxyhydantoin derivatives. Studies of a trinucleotide containing 5-hydroxyuracil suggest that the reactions described herein for the monomer can be extrapolated to DNA.     

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).     

The peak algebra and the descent algebras of types B and D

We show the existence of a unital subalgebra of the symmetric group algebra linearly spanned by sums of permutations with a common peak set, which we call the peak algebra. We show that is the image of the descent algebra of type B under the map to the descent algebra of type A which forgets the signs, and also the image of the descent algebra of type D. The algebra contains a two-sided ideal which is defined in terms of interior peaks. This object was introduced in previous work by Nyman (2003); we find that it is the image of certain ideals of the descent algebras of types B and D. We derive an exact sequence of the form . We obtain this and many other properties of the peak algebra and its peak ideal by first establishing analogous results for signed permutations and then forgetting the signs. In particular, we construct two new commutative semisimple subalgebras of the descent algebra (of dimensions and by grouping permutations according to their number of peaks or interior peaks. We discuss the Hopf algebraic structures that exist on the direct sums of the spaces and over and explain the connection with previous work of Stembridge (1997); we also obtain new properties of his descents-to-peaks map and construct a type B analog.

     

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.