An explicit compact universal space for real flows

The Kakutani–Bebutov Theorem (1968) states that any compact metric real flow whose fixed point set is homeomorphic to a subset of $\mathbb{R}$ embeds into the Bebutov flow, the $\mathbb{R}$-shift on $C(\mathbb{R},[0,1])$. An interesting fact is that this universal space is a function space. However, it is not compact, nor locally compact. We construct an explicit countable product of compact subspaces of the Bebutov flow which is a universal space for all compact metric real flows, with no restriction; namely, into which any compact metric real flow embeds. The result is compared to previously known universal spaces.     

Determination of Formaldehyde Traces in Fabric and in Indoor Air by a Kinetic Fluorimetric Method

A simple and sensitive kinetic fluorimetric method is reported for the determination of trace amount of formaldehyde. The proposed method is based on the catalytic effect of formaldehyde on the oxidation reaction of rhodamine B with potassium chlorate in sulfuric acid solution. Formaldehyde in the range of 0.020-0.340 µg/mL can be determined with a limit of detection of 5.73 ng/mL. The method has been used to determine trace formaldehyde in fabric and in indoor air. The results thus obtained show good agreement with those determined by acetyl acetone method.     

Synthesis,structural characterization and in vitro cytotoxic activity of novel polymeric triorganotin(IV) complexes of urocanic acid

Two novel triorganotin carboxylate complexes of the biologically active urocanic acid have been synthesized and characterized. Elemental analysis, melting point, spectroscopic techniques – IR, ¹H, ¹³C and ¹¹⁹Sn NMR – mass spectrometry and X‐ray diffraction studies have been used for structural characterization. Crystal structures of the tin(IV) derivatives show that urocanic acid acts as a bridging bidentate ligand through its imidazole nitrogen atom and its carboxylic group, producing a polymeric one‐dimensional chain. The molecular structures of the complexes, catena‐poly‐tri(n‐butyl)tin(IV) 3‐(3H‐imidazol‐4‐yl)prop‐2‐enoate (1) and catena‐poly‐triphenyltin(IV) 3‐(3H‐imidazol‐4‐yl)prop‐2‐enoate (2), present a distorted trigonal–bipyramidal configuration. This is further confirmed by ¹¹⁹Sn NMR in the solid state. The tin(IV) derivatives form double‐stranded ribbons via N―H^…O―H bonds. Nevertheless, the compounds are essentially monomeric in solution, with a tetrahedral configuration as observed by ¹¹⁹Sn NMR in solution. The cytotoxic activity of the titled compounds has been tested against six human cell lines and the corresponding IC₅₀ values are reported. Both tin(IV) compounds have a high to very high in vitro cytotoxic activity against the tumor cell lines K562, HCT‐15 and MCF‐7. Compound 1 is 86 times more active than cisplatin in the HTC‐15 cell line. Copyright © 2012 John Wiley & Sons, Ltd.     

Characterization of multispherical and block structures of Euclidean distance matrices

This paper presents some new characterizations of Euclidean distance matrices (EDMs) of special structures. More specifically, we discuss multispherical and block-structured EDMs, each of which can be viewed as a generalization of spherical EDM. We focus on a well-known inequality that characterizes spherical EDMs and extend it to the sets of multispherical and block-structured EDMs. Some related results are also presented.     

On reconstruction of objects from measurements of the diffracted field (*)

The aim of this paper is the shape restoration of a plane object from measurements of its diffracted field at a discrete and finite set of points. The plane sampling lattice is supposed: i) rectangular; ii)periodic.

The problem is approached as an interpolation one. A numerical algorithm for practical reconstructions is presented. A-priori limitations on the perimeter of the object and conditions on the samples lead to a-priori bounds able to estimate the precision of the reconstruction.     

Some remarks on the asymptotic behavor of toeplitz determinants

In order to optimize the stability regions we construct families of k multi-step methods with free parameters and of order k+1. We exhibit parameters for which the real interval of stability is arbitrarly large and using the Flexible Tolerance Method we show how these parameters optimize - under a predefined criterion - the stability region. Computational experience, while limited, has indicated that the procedure is efficient     

Generalized matching theorems for closed coverings of convex sets

In this paper we use fixed point and coincidence theorems due to Park [8] to give matching theorems concerning closed coverings of nonempty convex sets in a real topological vector space. Our new results extend previously given ones due to Ky Fan [2], [3], Shih [10], Shih and Tan [11], and Park [7].     

Assignment of complex species by affinity capillary electrophoresis: The case of Th(IV)-desferrioxamine B

The electrophoretic mobility change of desferrioxamine B (DFO) was monitored by UV absorption spectrophotometry upon increasing the thorium(IV) concentration in the background electrolyte at two acidities ([HClO₄]_Tot = 0.0316 and 0.0100 M). These data enabled to assess the speciation model and to determine the equilibrium constant of [Th(DFO)H₂]³⁺ at fixed ionic strength (I = 0.1 M (H,Na)ClO₄). Affinity capillary electrophoresis (ACE) turned out to be most helpful in identifying the complexed species by ascertaining its charge and protonation state. The assignment of the correct stoichiometry relied on the reliable estimation of the electrophoretic mobility by assuming similar hydrodynamic radii for (DFO)H₄⁺ and the chelate. The value of the apparent equilibrium constant (log β₁₁₂ = 38.7 ± 0.4) obtained by ACE compares favorably well with those reported in the literature for thorium and a range of other metal ions, according to a linear free-energy relationship. This method is useful for studying metal-ligand binding equilibria and provides valuable information for further modelling the behavior of tetravalent actinides under environmental conditions. Structural information about the prevalent solution species in acidic conditions was gained by DFT calculations, confirming the bishydroxamato coordination mode of Th⁴⁺ by the diprotonated ligand.