Sur la reéduction modulo p des polynoômes absolument irreéductibles

 On the reduction modulo p of absolutely irreducible polynomials. Let K be a number field and F(X,Y) be an absolutely irreducible polynomial of K[X,Y]. In this note, using an effective version of Riemann-Roch theorem and a version of the implicit functions theorem, we calculate a positive number A such that if ℘ is prime ideal of the ring of integers of K with norm , then the reduction of F(X,Y) modulo ℘ is an absolutely irreducible polynomial. (Réu le 1 Février 1999; en forme finale 21 Septembre 1999)     

Calabi–Yau Black Holes and (0,4) Sigma Models

When an M-theory fivebrane wraps a holomorphic surface › in a Calabi-Yau 3-fold X the low energy dynamics is that of a black string in 5 dimensional — =1 supergravity. The infrared dynamics on the string worldsheet is an — = (0,4) 2D conformal field theory. Assuming the 2D CFT can be described as a nonlinear sigma model, we describe the target space geometry of this model in terms of the data of X and ›. Variations of weight two Hodge structures enter the construction of the model in an interesting way.     

Stress field due to elastic mass growth on spherical and cylindrical substrates

Mass growth on cylindrical and spherical substrates is a phenomenon which can be related to the biochemical creation of an elastic actin gel shell by polymerization and cross linking of actin filaments either in vivo on bacteria cylindrical surfaces as a means for their motility or in vitro on spherical beads as a means for experimentally studying the previous in vivo case. Such mass growth is strongly effected by the developed stress field. The objective of this paper is to accurately determine this stress field assuming elasticity of the growing mass and symmetrical growth. Based on the special kinematics of mass growing on spherical and cylindrical substrates, inwards or outwards from them, and various isotropic constitutive laws for both small and finite elastic strains, it is possible to obtain the solution for the stress field in closed analytical form for all cases considered. This expands very significantly recent findings [Dafalias, Y.F., Pitouras, Z., 2008. Stress field in actin gel growing on spherical substrate. Biomechanics and Modeling in Mechanobiology, doi:10.1007/s10237-007-0113-y.] for some constitutive laws and outwards growth on spherical substrates only. The effect of biomass compressibility is shown to be of cardinal importance for the developed stress field, questioning the validity of the simplifying assumption of a zero value Poisson ratio usually made in the relevant biomechanics literature for simplicity. Few selected graphs of stress variation along the radial direction illustrate the analytical findings. The obtained closed form analytical expressions for stress can be a standard reference tool in this important area of stress-modulated soft tissue growth.     

Experimental and theoretical investigations of new dinuclear palladium complexes as precatalysts for the amination of aryl chlorides

A series of new palladium dinuclear species with general formula [Pd2X(mu-X)[mu-P(t)Bu2(Bph-R)]] (X = Cl, Br; Bph = biphenyl; R = H, Me, NMe2) have been prepared. The two palladium centers in these species are bridged by one of the aromatic rings of the biphenyl group present in the corresponding phosphine. The X-ray crystal structure of one of these complexes has been obtained, providing a clear picture of the bonding pattern. The stability of these dimers in solution is shown to be highly dependent on the nature of the phosphine R group and also on the bridging halide. When R = NMe2, the dimers dissociate, yielding the palladium(II) compounds PdX2[P(t)Bu2(BPh-NMe2)] (X = Cl, Br), and the X-ray crystal structure of one of them (X = Br) has shown that the biphenyl group from the phosphine interacts directly with the metal center. This interaction seems to play an important role in stabilizing the otherwise coordinatively unsaturated palladium(II) complex. In contrast, when R = H or Me, the analogous monomeric palladium(II) complexes are unstable and undergo cyclometalation to generate a palladium(II) dinuclear species in which each of the two phosphines cyclometalates with the palladium centers forming a strained four-membered ring. In addition to their unusual structures, these aryl-bridged dimers have also proven to be excellent precatalysts for the amination of aryl chlorides. To rationalize some of the experimental results, a detailed DFT computational study has been carried out and is presented herein.     

A three-state model for the polymorphism in linear tricobalt compounds

The remarkable polymorphism exhibited by the linear tricobalt compounds, Co3(mu3-dpa)4Cl2 and Co3(mu3-dpa)4Br2, can be explained using a model involving three distinct electronic states. At high temperatures, symmetric and unsymmetric forms arise from the population of doublet (2A) and quartet (4B) states, respectively, the latter containing a localized high-spin Co(II) center. In the unsymmetric form, a reduction in temperature leads to a spin-crossover to a second quite distinct doublet state, 2B, where, uniquely, the d(x2-y2) character on the localized Co(II) center is distributed between the occupied and vacant manifolds. The variable population of the Co d(x2-y2) orbital gives rise to the continuous change in Co-Co and Co-N bond lengths as the temperature is decreased.     

Magnetic anisotropy axis reorientation at ultrathin FePt films

Ultrathin FePt films (thickness between 1 nm and 5 nm) were studied for non‐volatile memories applications. The films were magnetron sputtered on monocrystalline MgO?001? substrates at 500 °C. The films are polycrystalline, except the 1 nm thick film which is not continuous. It is shown that films with thickness higher than 2.7 nm have L1₀ structure and perpendicular magnetic anisotropy, while a transition to in‐plane anisotropy occurs for thinner films. The out‐of‐plane coercivity drops from 16 kOe at the thicker film to 0.5 kOe at the thinner one.

Hysteresis cycles of FePt films as a function of film thickness.     

Large Plastic Deformation of Isotactic Poly(propylene) (iPP) Evaluated by WAXD Techniques

Summary: Commercial isotactic poly(propylene) (iPP), obtained in bars, was annealed and submitted to different levels of plastic deformation by uniaxial plane compression using a special device which permits well controlled temperature and strain rate. The evolution of the microstructure was followed at different degrees of deformation by wide angle x-ray diffraction (WAXD) techniques. The spherulite fragmentation process, lamellar orientation and destruction of the crystallites is argued, according to collected analytical data in the flow direction (FD), the loading direction (LD) and the lateral or constrain direction (CD). The evaluation of the WAXD patterns in terms of diffraction line position, intensity and width, permits to affirm that, while the large plastic deformation occurs, the crystalline net suffers anisotropic deformation, the crystallites become preferentially oriented along the flow direction and the crystalline phase diminish in amount indicating lesser and smaller crystallites. The gradual lamellae fragmentation occurs, starting with apparent crystalline size of approximately 30 nm for the non-deformed material and gradually decreasing to approximately 15 nm for the 70% deformed one.     

Size-selective protein adsorption to polystyrene surfaces by self-assembled grafted poly(ethylene glycols) with varied chain lengths

We report about the surface modification of polystyrene (PSt) with photoreactive alpha-4-azidobenzoyl-omega-methoxy poly(ethylene glycol)s (ABMPEG) of three different molecular weights (MWs of approximately 2, approximately 5, and approximately 10 kg/mol) and with two poly(ethylene glycol)/poly(propylene glycol) triblock copolymers (PEG-PPG-PEG) of about identical PEG/PPG ratio (80/20, w/w) and MW(PEG) of approximately 3 and approximately 6 kg/mol, all via adsorption from aqueous solutions. For ABMPEGs, an additional UV irradiation was used for photografting to the PSt. Contact angle (CA) and atomic force microscopy data revealed pronounced differences of the hydrophilicity/hydrophobicity and topography of the surfaces as a function of PEG type and concentration used for the modification. In all cases, an incomplete coverage of the PSt was observed even after modification at the highest solution concentrations (10 g/L). However, clear differences were seen between PEG-PPG-PEGs and ABMPEGs; only for the latter was a nanoscale-ordered interphase structure with an influence of MW(PEG) on the PEG density observed; after modification at the same solution concentrations, the density was significantly higher for lower MW(PEG). The adsorption of three proteins, myoglobin (Mgb), bovine serum albumin (BSA), and fibrinogen to the various surfaces was analyzed by surface plasmon resonance. Pronounced differences between the two PEG types with respect to the reduction of protein adsorption were found. At high, but still incomplete, surface coverage and similar CA, the shielding of ABMPEG layers toward the adsorption of Mgb and BSA was much more efficient; e.g., the adsorbed Mgb mass relative to that of unmodified PSt was reduced to 10% for ABMPEG 2 kg/mol while for both PEG-PPG-PEGs the Mgb mass was still around 100%. In addition, for the ABMPEG layers an effect of MW(PEG) on adsorbed protein mass-decrease with decreasing MW-could be confirmed; and the highest Mgb/BSA selectivities were also observed. A "two-dimensional molecular sieving", based on PEG molecules having a nanoscale order at the hydrophobic substrate polymer surface has been proposed, and the main prerequisites were the use of PEG conjugates which are suitable for an "end-on" grafting (e.g., ABMPEGs), the use of suitable (not too high) concentrations for the surface modification via adsorption/self-assembly, optionally the photografting on the substrate (possible only for ABMPEG), and presumably, a washing step to remove the excess of unbound PEGs. The results of this study also strongly support the hypothesis that the biocompatibility of hydrophobic materials can be very much improved by PEG modifications at surface coverages that are incomplete but have an ordered layer structure controlled by the size and steric interactions of surface-bound PEGs.     

Efficient syntheses of 5-aminoalkyl-1h-tetrazoles and of polyamines incorporating tetrazole rings

Linear N(omega)-tritylated omega-amino thiobenzylamides and N(alpha),N(omega)-ditritylated polyamino mono- or bisthioamides were efficiently converted to the corresponding tetrazole derivatives upon treatment with azidotrimethylsilane under Mitsunobu reaction conditions. [reaction: see text]