Rapid method for the preparation of a robust optical pH sensor

A simple and rapid method for the preparation of a fluorescence-based optical pH sensor is described. The sensor is based on excitation ratiometric detection of a methacryloyl-modified analog of the well-known fluorescent pH indicator dye, 8-hydroxy-1,3,6-pyrene trisulfonic acid (HPTS). The modified dye, 6-methacryloyl-8-hydroxy-1,3-pyrene disulfonic acid (MA-HPDS), is similar in structure and function to HPTS. However, unlike HPTS, the presence of the methacrylate moiety allows MA-HPDS to participate as a comonomer in a free radical polymerization reaction. Covalent immobilization by this method is simple, as the preparation of the modified dye is accomplished in a single reaction step and its subsequent reaction with a comonomer results in simultaneous immobilization and purification. Sensors were prepared by copolymerization of the MA-HPDS with poly(ethylene glycol) diacrylate. Minimal leaching of the immobilized dye was observed from the HPDS-PEG matrix. The copolymer of HPDS and PEG-DA is fully autoclavable. The sensor is useful over the pH range of 6-9, with excellent reproducibility. Ionic strength effects on the apparent pKa of the immobilized dye are small and predictable.     

Coadsorption of oxygen and acetylene on a clean iridium surface

The interaction between oxygen and acetylene is investigated at 140T500 K. Information on the reaction products is obtained from XPS and UPS studies of a surface covered with one of the reagents and exposed to the effect of the other. Carbon monoxide is the main product of C₂H₂ oxidation. The presence of adsorbed atomic oxygen is a necessary condition of the catalytic oxidation of C₂H₂ on Ir.

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140 KT500 K. XPS UPS , -. C₂H₂. C₂H₂ Ir.

     

High-resolution phonon study of the Ag(100) surface

Using high-resolution electron energy loss spectroscopy the phonon dispersion of Ag(100) has been studied at two different sample temperatures of 86 and 300 K. The dominant feature in the spectra corresponds to the Rayleigh wave. Its full dispersion is determined along the ΓX high symmetry direction in the first and second Brillouin zones. The Rayleigh phonon maximum at the X point shows a redshift with increasing temperature. This is explained based on a surface anharmonicity with an anharmonicity constant of 0.014, comparable to the value reported for Cu(100). In the vicinity of the Γ point two additional phonon features have been discovered at about 110 and 160 cm(-1), which are tentatively assigned to high density of states features from the bulk phonon bands. However, the observed steep dispersion is in contrast to theoretical calculations. Along ΓX two surface resonance branches have been observed with maximum frequencies in the range of 90-110 cm(-1) near to the zone boundary. These branches agree with helium atom scattering data where available, but are not predicted by theory.     

A mapping connected with the Schur–Szegő composition

Every monic polynomial in one variable of the form $(x+1)S$, $\mathrm{deg}S=n?1$, is presentable in a unique way as a Schur–Szeg? composition of $n?1$ polynomials of the form ${(x+1)}^{n?1}(x+a_i)$. We prove geometric properties of the affine mapping associating to the coefficients of S the $(n?1)$-tuple of values of the elementary symmetric functions of the numbers $a_i$. To cite this article: V.P. Kostov, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Narayana numbers and Schur–Szeg? composition

In the present paper we find a new interpretation of Narayana polynomials N_n(x) which are the generating polynomials for the Narayana numbers where stands for the usual binomial coefficient, i.e. . They count Dyck paths of length n and with exactly k peaks, see e.g. [R.A. Sulanke, The Narayana distribution, in: Lattice Path Combinatorics and Applications (Vienna, 1998), J. Statist. Plann. Inference 101 (1–2) (2002) 311–326 (special issue)] and they appeared recently in a number of different combinatorial situations, see for e.g. [T. Doslic, D. Syrtan, D. Veljan, Enumerative aspects of secondary structures, Discrete Math. 285 (2004) 67–82; A. Sapounakis, I. Tasoulas, P. Tsikouras, Counting strings in Dyck paths, Discrete Math. 307 (2007) 2909–2924; F. Yano, H. Yoshida, Some set partitions statistics in non-crossing partitions and generating functions, Discrete Math. 307 (2007) 3147–3160]. Strangely enough Narayana polynomials also occur as limits as n→∞ of the sequences of eigenpolynomials of the Schur–Szeg? composition map sending (n−1)-tuples of polynomials of the form (x+1)ⁿ⁻¹(x+a) to their Schur–Szeg? product, see below. We present below a relation between Narayana polynomials and the classical Gegenbauer polynomials which implies, in particular, an explicit formula for the density and the distribution function of the asymptotic root-counting measure of the polynomial sequence {N_n(x)}.     

Multicomponent nonlinear Schrödinger equations with constant boundary conditions

We outline several specific issues concerning the theory of multicomponent nonlinear Schrödinger equations with constant boundary conditions. We first study the spectral properties of the Lax operator L, the structure of the phase space \(\mathcal{M}\), and the construction of the fundamental analytic solutions. We then consider the regularized Wronskian relations, which allow analyzing the map between the potential of L and the scattering data. The Hamiltonian formulation also requires a regularization procedure.     

Sulphosalt minerals: Crystal chemistry and morphology

Polymerization of semi-metallic R₂S₃ and metallic (M²⁺M₂⁺)S structural units leads to step-like change of chemical composition of the sulphosalts and to morphology which is pronouncedly planar for the sulpharsenides, pseudoisometric for the sulphantimonides, and axial for the sulphobismuthides. Isomorphous substitution is very restricted both for semi-metals and metals.