Feasibility of diffusion-NMR surface-to-volume measurements tested by calculations and computer simulations

It has been demonstrated previously that the surface-to-volume ratio S/V can be determined from the derivative of the time-dependent diffusion coefficient D(t), in the limit t --> 0. Several questions arise concerning the practicality of determining S/V by NMR. In particular, how large are the errors generated by (1) working outside the t --> 0 limit and (2) measuring D outside the b --> 0 limit, both for narrow and full-width gradient pulses? Here b is gamma2G2delta2Delta for narrow pulses and gamma2G2t3/12 for broad pulses. These questions are addressed by random-walk computer simulations and numerical calculations in geometries relevant to small-airways of lung. The results demonstrate that one can work well outside the t --> 0 and b --> 0 limits, provided 10-20% accuracy in the measured S/V is sufficient. Emphasis is placed on the useful range of times t for which NMR determinations of lung S/V are feasible.     

Hartmann wave-front measurement at 13.4 nm with lambdaEUV/120 accuracy

We report, for the first time to our knowledge, experimental demonstration of wave-front analysis via the Hartmann technique in the extreme ultraviolet range. The reference wave front needed to calibrate the sensor was generated by spatially filtering a focused undulator beam with 1.7- and 0.6-microm-diameter pinholes. To fully characterize the sensor, accuracy and sensitivity measurements were performed. The incident beam's wavelength was varied from 7 to 25 nm. Measurements of accuracy better than lambdaEUV/120 (0.11 nm) were obtained at lambdaEUV = 13.4 nm. The aberrations introduced by an additional thin mirror, as well as wave front of the spatially unfiltered incident beam, were also measured.     

A tetranuclear Cr(III)Ni(II)3 cyano-bridged complex based on M(tacn) derivative building blocks

The reaction of Cr(Bztacn)(CN)3 (Bztacn is 1,4,7-trisbenzyl-1,4,7-triazacyclononane) with Ni(iPrtacn)Cl2 (iPrtacn is 1,4,7-trisisopropyl-1,4,7-triazacyclononane) affords a CrNi3 tetranuclear complex. Variable temperature and magnetization versus field measurements show a S = 9/2 ground state and an appreciable magnetic anisotropy with a negative D(9/2) value equal to -0.54 cm(-1). Magnetization studies on one single crystal using a micro-SQUID show a fast tunneling process at zero field at very low temperature.     

perpendicular organization of macromolecules: synthesis and alignment studies of a soluble poly(iptycene)

We describe herein a polymeric material that prefers to align perpendicular to a stretch-aligned polymer host in the solid state. Poly(iptycene) poly-1 was synthesized from monomer 1 under hyperbaric techniques via a Diels-Alder polymerization. Polarized excitation spectra of the anthracene end groups in this material in a stretch-aligned, solution-cast poly(vinyl chloride) (PVC) film showed that the poly(iptycene) prefers to align normal (counter aspect ratio) to the stretching direction of the PVC. This is explained by a "threading" mechanism, whereby the PVC intercalates through the internal free volume presented by poly-1, similar to effects observed in small molecule iptycenes under similar conditions.     

Cyclic maps in rational homotopy theory

The notion of a cyclic map g:AX is a natural generalization of a Gottlieb element in _n(X). We investigate cyclic maps from a rational homotopy theory point of view. We show a number of results for rationalized cyclic maps which generalize well-known results on the rationalized Gottlieb groups.Mathematics Subject Classification (2000): 55P62, 55Q05     

D.C. Versus Copositive Bounds for Standard QP

The standard quadratic program (QPS) is min_xεΔx^TQx, where is the simplex Δ = {x ⩽ 0 ∣ ∑_i=1ⁿ x_i = 1}. QPS can be used to formulate combinatorial problems such as the maximum stable set problem, and also arises in global optimization algorithms for general quadratic programming when the search space is partitioned using simplices. One class of ‘d.c.’ (for ‘difference between convex’) bounds for QPS is based on writing Q=S−T, where S and T are both positive semidefinite, and bounding x^T Sx (convex on Δ) and −x^Tx (concave on Δ) separately. We show that the maximum possible such bound can be obtained by solving a semidefinite programming (SDP) problem. The dual of this SDP problem corresponds to adding a simple constraint to the well-known Shor relaxation of QPS. We show that the max d.c. bound is dominated by another known bound based on a copositive relaxation of QPS, also obtainable via SDP at comparable computational expense. We also discuss extensions of the d.c. bound to more general quadratic programming problems. For the application of QPS to bounding the stability number of a graph, we use a novel formulation of the Lovasz ϑ number to compare ϑ, Schrijver’s ϑ′, and the max d.c. bound.     

L'électron habillé non relativiste dans un champ magnétique

We consider a nonrelativistic electron interacting with a classical magnetic field pointing along the $x_3$-axis and with a quantized electromagnetic field. Because of the translation invariance along the $x_3$-axis, we consider the reduced Hamiltonian associated with the total momentum along the $x_3$-axis and, after introducing an ultraviolet cutoff and an infrared regularization, we prove that the reduced Hamiltonian has a ground state if the coupling constant and the total momentum along the $x_3$-axis are sufficiently small. Finally, we determine the absolutely continuous spectrum of the reduced Hamiltonian and we prove that the renormalized mass of the electron is greater than its bare one. To cite this article: L. Amour et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Septal repair implants: evaluation of magnetic resonance imaging safety at 3 T

Specialized implants are used for transcatheter closure of septal defects, including atrial and ventricular septal defects, and patent foramen ovale. These metallic devices may pose a risk to patients undergoing magnetic resonance imaging (MRI) procedures especially if performed at 3 T. Therefore, this investigation evaluated MRI safety at 3 T for septal repair implants (CardioSEAL Septal Repair Implant and STARFlex Septal Repair Implant, NMT Medical, Boston, MA, USA) by characterizing magnetic field interactions, heating and artifacts. These implants exhibited minor magnetic field interactions; heating was not excessive (+0.5°C); and artifacts will only create a problem if the area of interest is in the same area as or near these devices. Thus, the findings indicated that it would be safe for a patient with these implants to undergo MRI at 3 T or lower. Importantly, because of the minor magnetic field interactions, MRI may be performed immediately after implantation.     

Coating of poly(dimethylsiloxane) with n-dodecyl-beta-D-maltoside to minimize nonspecific protein adsorption

Poly(dimethylsiloxane)(PDMS) surface is coated with n-dodecyl-beta-D-maltoside, which reduces the nonspecifically adsorbed protein on the PDMS surface to the single molecule level.