On the Froissart phenomenon in multivariate homogeneous Padé approximation

In univariate Padé approximation we learn from the Froissart phenomenon that Padé approximants to perturbed Taylor series exhibit almost cancelling pole–zero combinations that are unwanted. The location of these pole–zero doublets was recently characterized for rational functions by the so‐called Froissart polynomial. In this paper the occurrence of the Froissart phenomenon is explored for the first time in a multivariate setting. Several obvious questions arise. Which definition of Padé approximant is to be used? Which multivariate rational functions should be investigated? When considering univariate projections of these functions, our analysis confirms the univariate results obtained so far in [13], under the condition that the noise is added after projection. At the same time, it is apparent from section 4 that for the unprojected multivariate Froissart polynomial no conjecture can be formulated yet.

     

Tuneable fluorescent marker appended to β-cyclodextrin: a pH-driven molecular switch

The photophysical properties of a pH dependent molecular switch based on pyridin-4-yl indolizin β-cyclodextrin 1 in water are described. The reversibility phenomena of fluorescent emission is attributed to a molecular motion of enclosed fluorescent moiety to inside/outside location.     

On the fast solution of Toeplitz-block linear systems arising in multivariate approximation theory

When constructing multivariate Padé approximants, highly structured linear systems arise in almost all existing definitions [10]. Until now little or no attention has been paid to fast algorithms for the computation of multivariate Padé approximants, with the exception of [17]. In this paper we show that a suitable arrangement of the unknowns and equations, for the multivariate definitions of Padé approximant under consideration, leads to a Toeplitz-block linear system with coefficient matrix of low displacement rank. Moreover, the matrix is very sparse, especially in higher dimensions. In Section 2 we discuss this for the so-called equation lattice definition and in Section 3 for the homogeneous definition of the multivariate Padé approximant. We do not discuss definitions based on multivariate generalizations of continued fractions [12, 25], or approaches that require some symbolic computations [6, 18]. In Section 4 we present an explicit formula for the factorization of the matrix that results from applying the displacement operator to the Toeplitz-block coefficient matrix. We then generalize the well-known fast Gaussian elimination procedure with partial pivoting developed in [14, 19], to deal with a rectangular block structure where the number and size of the blocks vary. We do not aim for a superfast solver because of the higher risk for instability. Instead we show how the developed technique can be combined with an easy interval arithmetic verification step. Numerical results illustrate the technique in Section 5.Research partly funded by FWO-Vlaanderen.     

Efficient synthesis of amino-protected calix[4]arenes selectively functionalized with iron chelator ICL670 designed as platform for iron recognition

The development of selective electrochemical iron sensor is still a challenging task. One promising possibility is to use organically functionalized inorganic particles, for instance silica, as sensitive element. Herein, we report on the design and synthesis of calix[4]arene-based platforms modified with ICL670 iron chelator and alkylamino chain(s). These new molecular edifices could be easily grafted on silica particles. The strategy relies on selective calix[4]arenes functionalizations by alkylamino chains at the lower rim, in partial-cone or 1,3-alternate conformations. The different synthesis routes are presented and discussed.     

Calix[4]arene-modified silica nanoparticles for the potentiometric detection of iron (III) in aqueous solution

This article aims to present the synthesis and the characterization of a novel hybrid material, based on silica nanoparticles, and which can be used as a sensitive element for the electrochemical detection of iron (III). This material was obtained by grafting an iron ligand-based calix[4]arene structure onto nanosized silica particles. The covalent anchoring of the chelator was obtained by nucleophilic coupling reaction between the modified calix[4]arene and the chloropropyl functionalized silica. The grafting reaction was confirmed by FTIR (DRIFT), solid-state ¹³C Cross-Polarization MAS (CPMAS) NMR and thermal analysis. The interaction between the material and the dissolved iron (III) was demonstrated though potentiometric measurements. A linear evolution of the open circuit potential, which can be used analytically for iron (III) detection, has been obtained.