The Helmholtz equation with impedance in a half-space

In this Note we obtain existence and uniqueness results for the Helmholtz equation in the half-space ${\mathbb{R}}_{+}^3$ with an impedance or Robin boundary condition. Basically, we follow the procedure we have already used in the bi-dimensional case (the half-plane). Thus, we compute the associated Green's function with the help of a double Fourier transform and we analyze its far field in order to obtain radiation conditions that allow us to prove the uniqueness of an outgoing solution. Again, these radiation conditions are somewhat unusual due to the appearance of a surface wave guided by the boundary. An integral representation of the solution is presented by means of the Green's function and the boundary data. To cite this article: M. Durán et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

The impact of metrological traceability on the validity of creatinine measurement as an index of renal function

When the calibration of a routine measurement procedure is traced back to metrological higher order, a significant discrepancy can occur between the analytical conditions of the routine measurement and the analytical conditions that were used in the clinical studies upon which the decision-making criteria are based. This can lead to serious interpretation errors with possible dramatic consequences for patients. The calibration of the creatinine Jaffé method is an excellent example of the importance of medical traceability. The compensated Jaffé method correlated accurately with the reference method and the compensated Jaffé creatinine clearance (CrCl), Cockroft and Gault and MDRD with the ⁵¹Cr EDTA clearance. The Schwartz estimate based upon the compensated Jaffé and enzymatic method overestimated, while uncompensated Jaffé slightly underestimated glomerular filtration rate (GFR). The situation in children is complex since serum creatinine concentrations are much lower in infants, rendering tubular secretion relatively more important. Low-molecular weight proteins have been suggested to replace serum creatinine as a marker for GFR. -trace protein, cystatin C, and ₂-microglobulin showed good correlation with GFR. However, care should be taken in patients presenting with some malignant tumors, since significant increases of cystatin C in patients with metastatic melanoma or colorectal cancer has been reported.Presented at the 9th Conference on Quality in the Spotlight, 18-19 March 2004, Antwerp, Belgium     

Simultaneous freezing of chirality and in-out conformation of a macropentacyclic cryptand by protonation

Compound 1, a cryptand-derived macropentacycle, is a flexible molecule that encompasses many conformations (symmetrical, unsymmetrical, and chiral ones) depending on the observation temperature (VT 1H NMR). Selective monoprotonation of this molecule leads to a totally unsymmetrical, rigidly chiral species in solution (1H NMR). Helical chirality and in-out conformation of monoprotonated 1 are observed in the solid state by X-ray diffraction analysis, as well as the proton location. The latter is bound to the endo bridgehead nitrogen atom and involved in hydrogen-bonding interactions with the three closest sulfurs. Significant induction of chirality is triggered by reaction of 1 with the optically active (R)-(-)-1,1'-binaphthyl-2,2'-diylphosphoric acid. It proceeds with a maximum 24% diastereomeric excess, as shown by the splitting, in the 62:38 intensity ratio, of several 1H NMR signals. These correspond to the two indistinguishable diastereomeric ion pairs: (Lambda-[1-H])((R)-(-)-BNP) and (Delta-[1-H])((R)-(-)-BNP).     

Redox-triggered molecular movement in a multicomponent metal complex in solution and in the solid state

The Cu(I) and Cu(II) complexes of the new 1,8-diferro-cenylmethyl-4,11-dimethyl-1,4,8,11-tetraazacyclotetra-decane ligand (denoted L) have been isolated and characterized by X-ray structure determination and electrochemical studies. The Cu(I) complex presents an unprecedented stability toward dioxygen. The two complexes adopt two energetically distinct and stable geometries, which differ mainly by the relative positioning of the substituents above or below the cyclam plane. Triggered by a copper-centered electron transfer, a fast and reversible motion of the noncoordinating subunits is obtained in homogeneous solution and in the solid state.     

Dynamic arsenic removal on a MnO2-loaded resin

Previous batch studies on a polystyrene matrix loaded with manganese dioxide, synthesized from an anionic commercial resin in chloride form, have proven the efficiency of this sorbent in As(V) and As(III) removal. This solid is now tested with column experiments to predict its behavior in a treatment process. An artificial water, with a composition in major ions similar to that of granitic water, often contaminated with arsenic, was prepared. This artificial water was used to simulate arsenic removal processes under near-natural conditions and with a stable composition. Furthermore, the hydride generation AAS analytical method was optimized to measure low arsenic concentrations (1 to 20 microg/L).     

Monoid of self-equivalences and free loop spaces

Let be a simply-connected closed oriented -dimensional manifold. We prove that for any field of coefficients there exists a natural homomorphism of commutative graded algebras where is the loop algebra defined by Chas and Sullivan. As usual denotes the monoid of self-equivalences homotopic to the identity, and the space of based loops. When is of characteristic zero, yields isomorphisms where denotes the Hodge decomposition on .

     

Functionalization of polyoxometalates: from Lindqvist to Keggin derivatives. 1. synthesis, solution studies, and spectroscopic and ESI mass spectrometry characterization of the rhenium phenylimido tungstophosphate [PW11O39(ReNC6H5)]4-

Reaction of [Bu(4)N](4)[H(3)PW(11)O(39)] with [Re(NPh)Cl(3)(PPh(3))(2)], in acetonitrile and in the presence of NEt(3), provided the first Keggin-type organoimido derivative [Bu(4)N](4)[PW(11)O(39)(ReNPh)] (Ph = C(6)H(5)) (1). The functionalization was clearly demonstrated by various techniques including (1)H and (14)N NMR, electrochemistry, and ESI mass spectrometry. Conditions for the formation of 1 are also discussed.     

Tunable coupling of superconducting qubits

We study an LC circuit implemented using a current-biased Josephson junction (CBJJ) as a tunable coupler for superconducting qubits. By modulating the bias current, the junction can be tuned in and out of resonance and entangled with the qubits coupled to it. One can thus implement two-qubit operations by mediating entanglement. We consider the examples of CBJJ and charge-phase qubits. A simple recoupling scheme leads to a generalization to arbitrary qubit designs.     

Solid-state glycation of beta-lactoglobulin monitored by electrospray ionisation mass spectrometry and gel electrophoresis techniques

Glycation of beta-lactoglobulin (beta-Lg) with either lactose or galactose in a solid-state medium was monitored using gel electrophoresis techniques and liquid chromatography coupled to electrospray ionisation mass spectrometry (LC/ESI-MS). The kinetics of glycation monitored by SDS polyacrylamide gel electrophoresis showed a molecular weight increase over time of the beta-Lg bands for both sugars, but no significant amounts of aggregated proteins were observed. The isoelectric point of the protein, observed by isoelectric focusing gel electrophoresis, was dramatically affected by galactosylation. LC/MS measurements of beta-Lg variants A and B, over the whole glycation reaction time, showed a larger extent of glycation with galactose (from 4 up to 22 adducts) as compared with lactose (from 0 up to 14 adducts), and confirmed that early Maillard reaction products were the main species observed. Based on the relative abundances obtained from the deconvoluted mass spectra after a 8 h 15 min incubation time at 60 degrees C, the mean values of lactose and galactose molecules bound to the protein species were calculated to be 10.4 and 17.9, and 10.5 and 18.6, for variants A and B, respectively. Furthermore, the charge state distribution data obtained by ESI-MS was studied using different methanol percentages, and indicated that adduct formation with lactose, but more significantly galactose, tends to improve the stability properties of the native protein towards denaturation.     

The first self-assembled trimetallic lanthanide helicates driven by positive cooperativity

The segmental tris-tridentate ligand L7 reacts with stoichiometric quantities of Ln(III) (Ln=La-Lu) in acetonitrile to give the complexes [Ln(2)(L7)(3)](6+) and [Ln(3)(L7)(3)](9+). Formation constants point to negligible size-discriminating effects along the lanthanide series, but Scatchard plots suggest that the self-assembly of the trimetallic triple-stranded helicates [Ln(3)(L7)(3)](9+) is driven to completion by positive cooperativity, despite strong intermetallic electrostatic repulsions. Crystallization provides quantitatively [Ln(3)(L7)(3)](CF(3)SO(3))(9) (Ln=La, Eu, Gd, Tb, Lu) and the X-ray crystal structure of [Eu(3)(L7)(3)](CF(3)SO(3))(9).(CH(3)CN)(9).(H(2)O)(2) (Eu(3)C(216)H(226)N(48)O(35)F(27)S(9), triclinic, P1, Z=2) shows the three ligand strands wrapped around a pseudo-threefold axis defined by the three metal ions rigidly held at about 9 A. Each metal ion is coordinated by nine donor atoms in a pseudo-trigonal prismatic arrangement, but the existence of terminal carboxamide units in the ligand strands differentiates the electronic properties of the terminal and the central metallic sites. Photophysical data confirm that the three coordination sites possess comparable pseudo-trigonal symmetries in the solid state and in solution. High-resolution luminescence analyses evidence a low-lying LMCT state affecting the central EuN(9) site, so that multi-metal-centered luminescence is essentially dominated by the emission from the two terminal EuN(6)O(3) sites in [Eu(3)(L7)(3)](9+). New multicenter equations have been developed for investigating the solution structure of [Ln(3)(L7)(3)](9+) by paramagnetic NMR spectroscopy and linear correlations for Ln=Ce-Tb imply isostructurality for these larger lanthanides. NMR spectra point to the triple helical structure being maintained in solution, but an inversion of the magnitude of the second-rank crystal-field parameters, obtained by LIS analysis, for the LnN(6)O(3) and LnN(9) sites with respect to the parameters extracted for Eu(III) from luminescence data, suggests that the geometry of the central LnN(9) site is somewhat relaxed in solution.