Representation of the category of tangles by Kontsevich's iterated integral

Applying Kontsevich's iterated integral for tangles, we get an isotopy invariant of tangles. We give a method to compute the integral of a tangle combinatorially from modified integrals of some simple tangles. We localize the integral by moving the end points of the tangle to an extreme configuration, and modify the integral so that it is convergent. By using a similar technique, we generalize Kontsevich's invariant to a framed tangle.     

Fonctions L associées aux F-isocristaux surconvergents II: Zéros et pôles unités

Résumé Nous démontrons la conjecture de Katz concernant la méromorphie et la caractérisation des zéros et p?les unités des fonctions L associées aux représentations p-adiques lorsque celles-ci se prolongent sur une compactification du schéma de base. Comme cas particuliers importants, on obtient celui de la fonction zêta d’un schéma quelconque et celui d’une représentation p-adique quelconque sur un schéma propre.

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If X is a smooth variety over a finite field ? _q of characteristic p > 0 and ℱ is a p-adic sheaf associated to a representation of the fundamental group of X, N. Katz conjectures, in his Bourbaki talk 409, that the L function L (X, ℱ, t) has its p-adic unit roots and poles given in terms of p-adic étale cohomology. We prove this conjecture in the case of the structure sheaf ℱ = ℤ _p , that is for the Zeta function, and also more generally when the p-adic sheaf ℱ extends to a smooth sheaf on a compactification of X: as a consequence we get the Unit-Root Zeta function of Dwork and Sperber as an L function. The idea of the proof is to get the p-adic étale cohomology with coefficients and compact support as the fixed points of Frobenius acting on rigid cohomology with compact support. For this purpose, we first build a crystalline Artin–Schreier short exact sequence on the syntomic site of a scheme which is separated of finite type over a perfect field k: this naturally generalizes the work of J.M. Fontaine and W. Messing in the proper smooth case. Then getting rigid cohomology with coefficients as a limit of crystalline cohomologies of variable level we deduce a long exact sequence connecting p-adic étale cohomology (with compact support) to rigid cohomology (with compact support). When X is smooth and affine over an algebraically closed field, the former exact sequence splits into short exact sequences that identify the p-adic étale cohomology with support of X to the part of its rigid cohomology invariant under Frobenius. We can then describe the p-adic unit roots and poles of the Zeta function of X; as a corallary we get the Unit-Root Zeta function of Dwork and Sperber as an L function. In the appendix we show that the characteristic spaces of Frobenius in rigid cohomology commute with isometric extensions of the base, and that isocrystals associated to p-adic sheaves with finite monodromy are overconvergent: we thus obtain a p-adic proof of the rationality of the corresponding L-function.

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Oblatum 8-XII-1994 & 30-IV-1996     

On some natural and model 2D bimodal random cellular structures

The topological and metric properties of a few natural 2D random cellular structures, namely an armadillo shell structure and young soap froths, which are formed from two classes of cells, large and small, have been characterized. The topological properties of a model generated from a Kagome tiling, which mimics such random binary structures, have also been exactly calculated. The distribution of the number of cell sides is bimodal for the structures investigated. In contrast to the classical Aboav-Weaire law for homogeneous 2D random cellular structures, nm(n), the mean total number of edges of neighbouring cells of cells with n sides does not vary linearly with n. Only the nm(i, n) (i=1,2) determined separately for every class of cells are linear in n for all investigated structures. Topological properties and correlations between metric and topological properties are finally compared with the predictions of various literature models. Received: 24 December 1997 / Revised: 7 April 1998 / Accepted: 20 April 1998     

Additive quark model of multiparticle production and α-α interactions at ISR energies

Using a specific version of the additive quark model we compute the relative (to proton-proton) single particle rapidity distributions for particles produced in α-α interactions at CERN ISR energies.     

Microbiological transformations 2. Hydroxylations of non activated carbons in globular type amides.

This paper describes the regioselective biohydroxylation of 7-azabrendane and 6-azatwistane derivatives.     

Measurement and interpretation of the 1-0 band of 14N16O at 1900 cm−1

The wavenumbers of the vibration rotation band lines of ¹⁴N¹⁶O are reported for the ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{-}{}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{-}{}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{-}{}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ subbands of the 1-0 transition in the infrared. The full set of spectroscopic constants for this band has been determined by direct approach using the analysis of Zare, Schmeltekopf, Harrop, and Albritton. In addition to the band origin ν₀ and the B, D, H constants for the lower and upper vibrational levels, the following spin-orbit coupling constants have been derived: $\text{A}\text{?}{}_0\text{= 123.02772 ± 0.00011}$ and $\text{A}\text{?}{}_1\text{= 122.78248 ± 0.00011}$ (in cm^?1). Apparent centrifugal corrections to these constants have been determined and the values obtained for them are $\text{A}\text{?}{}_{\mathrm{<mtext>D</mtext><mtext>0</mtext>}}\text{= (0.347573 ± 0.00051) × 10}{}^{\mathrm{?3}}$ and $\text{A}\text{?}{}_{\mathrm{<mtext>D</mtext><mtext>1</mtext>}}\text{= (0.337135 ± 0.00050) × 10}{}^{\mathrm{?3}}\text{cm}{}^{\mathrm{?1}}$. Λ-Type doubling constants evaluated by using both grating and tunable laser data are also reported.     

A statistical model for transitions in nematic liquid crystals

The two-lattice model of Lennard-Jones and Devonshire has been modified and applied to the study of the transition from the nematic to the isotropic phase. We have used the concept of external degrees of freedom for molecules introduced by Prigogine and applied to the case of chain liquids.