A Carleman estimate for the linear magnetoelastic waves system and an inverse source problem in a bounded conductive medium

ABSTRACT

In this paper, we consider an inverse problem for the simultaneous diffusion process of elastic and electromagnetic waves in an isotropic heterogeneous elastic body which is identified with an open bounded domain. From the mathematical point of view, the system under consideration can be viewed as the coupling between the hyperbolic system of elastic waves and a parabolic system for the magnetic field. We study an inverse problem of determining the external source terms by observations data in a neighborhood of the boundary and we prove the Hölder stability. For the proof, we show a Carleman estimate for the displacement and the magnetic field of the magnetoelastic system.     

1,3‐Alternate Tetraamido‐Azacalix[4]arenes as Selective Anion Receptors

Six tetraaza[1.1.1.1]cyclophane derivatives bearing peripheral amide groups were prepared according to two distinct synthetic strategies that depend on the connection pattern between the aryl units. NMR experiments combined with the X‐ray structures of two tetraamide derivatives 4 b and 10 show that these cavitands adopt a 1,3‐alternate conformation both in solution and in the solid state. Consequently, the four amide groups of the aza[1.1.1.1]‐m,m,m,m‐cyclophane isomer 10 can contribute to the same recognition process towards neutral water molecules or anion guests. NMR experiments, mass spectrometry analyses and single‐crystal X‐ray structures confirm the anion‐binding ability of this receptor. Absorption spectrophotometric titrations in nonpolar solvents provided evidence for the selectivity of 10 to chloride anions in the halide series, with a corresponding association constant K_a reaching 2.5×10⁶ m ^?1.     

Mixed Wavelet Leaders Multifractal Formalism in a Product of Critical Besov Spaces

In this paper, we will prove (resp. study) the Baire generic validity of the upper-Hölder (resp. iso-Hölder) mixed wavelet leaders multifractal formalism on a product of two critical Besov spaces \(B_{t_{1}}^{\frac{m}{t_{1}},q_{1}}(\mathbb {R}^m) \times B_{t_{2}}^{\frac{m}{t_{2}},q_{2}}(\mathbb {R}^m)\), for \(t_1,t_2>0\), \(q_1 \le 1\) and \(q_2 \le 1\). Contrary to product spaces \(B_{t_{1}}^{s_{1},\infty }(\mathbb {R}^m) \times B_{t_{2}}^{s_{2},\infty }(\mathbb {R}^m) \) with \(s_{1} > \frac{m}{t_{1}}\) and \(s_{2} >\frac{m}{t_{2}}\) (Ben Slimane in Mediterr J Math, 13(4):1513–1533, 2016) and \((B_{t_{1}}^{s_{1},\infty }(\mathbb {R}^m) \cap C^{\gamma _{1}}(\mathbb {R}^m)) \times (B_{t_{2}}^{s_{2},\infty }(\mathbb {R}^m) \cap C^{\gamma _{2}}(\mathbb {R}^m)\) with \(0<\gamma _{1}<s_{1}<\frac{m}{t_{1}}\) and \(0<\gamma _{2}<s_{2}<\frac{m}{t_{2}}\) (Ben Abid et al. in Mediterr J Math, 13(6):5093–5118, 2016), all pairs of functions in the obtained generic set are not uniform Hölder. Nevertheless, the characterization of the upper bound of the Hölder exponent by decay conditions of local wavelet leaders suffices for our study.     

On the Calderón problem in periodic cylindrical domain with partial Dirichlet and Neumann data

We consider the Calderón problem in an infinite cylindrical domain, whose cross section is a bounded domain of the plane. We prove log–log stability in the determination of the isotropic periodic conductivity coefficient from partial Dirichlet data and partial Neumann boundary observations of the solution. Copyright © 2017 John Wiley & Sons, Ltd.     

Radical‐Cation Dimerization Overwhelms Inclusion in [n]Pseudorotaxanes

Suppression of the dimerization of the viologen radical cation by cucurbit[7]uril ( CB7 ) in water is a well‐known phenomenon. Herein, two counter‐examples are presented. Two viologen‐containing thread molecules were designed, synthesized, and thoroughly characterized by ¹H DOSY NMR spectrometry, UV/Vis absorption spectrophotometry, square‐wave voltammetry, and chronocoulometry: BV ⁴⁺, which contains two viologen subunits, and HV ¹²⁺, which contains six. In both threads, the viologen subunits are covalently bonded to a hexavalent phosphazene core. The corresponding [3]‐ and [7]pseudorotaxanes that form on complexation with CB7 , that is, BV ⁴⁺?( CB 7)₂ and HV ¹²⁺?( CB 7)₆, were also analyzed. The properties of two monomeric control threads, namely, methyl viologen ( MV ²⁺) and benzyl methyl viologen ( BMV ²⁺), as well as their [2]pseudorotaxane complexes with CB7 ( MV ²⁺? CB7 and BMV ²⁺? CB7 ) were also investigated. As expected, the control pseudorotaxanes remained intact after one‐electron reduction of their viologen‐recognition stations. In contrast, analogous reduction of BV ⁴⁺?( CB 7)₂ and HV ¹²⁺?( CB 7)₆ led to host–guest decomplexation and release of the free threads BV ^{2( . +)} and HV ^{6( . +)}, respectively. ¹H DOSY NMR spectrometric and chronocoulometric measurements showed that BV ^{2( . +)} and HV ^{6( . +)} have larger diffusion coefficients than the corresponding [3]‐ and [7]pseudorotaxanes, and UV/Vis absorption studies provided evidence for intramolecular radical‐cation dimerization. These results demonstrate that radical‐cation dimerization, a relatively weak interaction, can be used as a driving force in novel molecular switches.     

Conductivity and dielectric relaxation in various polyvinyl alcohol/ammonium salt composites

We studied electrical conductivity and dielectric relaxation in polyvinyl alcohol/ammonium chloride and polyvinyl alcohol/ammonium acetate composite films. Infrared absorbance showed the presence of H-bonding interaction between the salt and the polymer. X-ray diffraction showed the reduction of the grain size of ordered regions in the polymer matrix after adding salt. Thermo gravimetric analysis (TGA) showed water wt% content between 4.2 and 5.8%. Differential Scanning Calorimetry (DSC) showed the decrease of the glass transition due to retained water indicating its plasticizer effect. The ac conductivity studied in the frequency range from 10^?1 Hz to 1 MHz and the temperature range from 10 to 150°C is described by the universal law of Jonsher characterizing the charge transport in disordered materials. With NH₄Cl inclusion, the dc conductivity showed a higher value in the vicinity of 4% but with NH₄CH₃CO₂ the dc conductivity decreases monotonically by increasing the salt amount. By using the dielectric permittivity and dielectric modulus we detected three relaxation processes which we attributed to electrode/sample polarization, alpha relaxation and conductivity relaxation respectively.     

Adsorption equilibrium studies for O‐xylene vapour and modified clays system

Tunisian bentonites were used to prepare three modified clays: two organoclays by intercalating respectively didodecyldimethylammoniumbromide (DDMAC) and hexadecyltrimethylammoniumbromide (HDTMAC), and synthesis of NaX zeolite. The X‐ray diffraction, infrared and thermogravimetric analyses enabled us to differentiate between the structures obtained. Clay materials systems were used as adsorbent for the investigation of the adsorption isotherms and saturation capacity of O‐xylene, a toxic volatile organic compound, by gravimetric method at three different temperatures 20, 30, and 40 °C. The absolute values of the volatile organic compound adsorbed amounts in the intercalated clays (604 mg g^?1) were higher than for the zeolite (296 mg g^?1). The adsorption isotherms were analysed by the Freundlich and Langmuir equations. The latter was found to describe better the equilibrium adsorption data. Mass transfer coefficient of O‐xylene is evaluated using uptake curve method, and all values are in the order of 10^?2 s^?1. Copyright © 2014 John Wiley & Sons, Ltd.     

A Novel Screen-Printed and Carbon Paste Electrodes for Potentiometric Determination of Uranyl(II) Ion in Spiked Water Samples

Four new ion-selective electrodes (ISEs) based on poly-(1-4)-2-amino-2-deoxy-β-D-glucan (chitosan) ionophore were constructed for determination of uranyl ion (UO₂(II)) over wide concentration ranges. The linear concentration range for carbon paste electrodes (CPEs) was 1 × 10^–6–1 × 10^–2 mol/L with a detection limit of 1 × 10^–6 mol/L and that for the screen-printed electrode (SPEs) was 1 × 10^–5–1 × 10^–1 mol/L with a detection limit of 8 × 10^–6 mol/L. The slopes of the calibration graphs were 29.90 ± 0.40 and 29.10 ± 0.60 mV/decade for CPEs with dibutylphthalate (DBP) (electrode I) and o-nitrophenyloctylether (o-NPOE) (electrode II) as plasticizers, respectively. Also, the SPEs showed good potentiometric slopes of 29.70 ± 0.30 and 28.20 ± 1.20 mV/decade with DBP (electrode III) and o-NPOE (electrode IV), respectively. The electrodes showed stable and reproducible potential over a period of 54, 62, 101 and 115 days for electrodes I, II, III, and IV, respectively. The electrodes manifested advantages of low resistance, very fast response and, most importantly, good selectivities relative to a wide variety of other cations except Ce(III) ion which interfere seriously. The results obtained compared well with those obtained using atomic absorption spectrometry.     

Reactivity of molecular dioxygen towards a series of isostructural dichloroiron(III) complexes with tripodal tetraamine ligands: general access to mu-oxodiiron(III) complexes and effect of alpha-fluorination on the reaction kinetics

We have synthesized the mono, di-, and tri-alpha-fluoro ligands in the tris(2-pyridylmethyl)amine (TPA) series, namely, FTPA, F(2)TPA and F(3)TPA, respectively. Fluorination at the alpha-position of these nitrogen-containing tripods shifts the oxidation potential of the ligand by 45-70 mV per added fluorine atom. The crystal structures of the dichloroiron(II) complexes with FTPA and F(2)TPA reveal that the iron center lies in a distorted octahedral geometry comparable to that already found in TPAFeCl(2). All spectroscopic data indicate that the geometry is retained in solution. These three isostructural complexes all react with molecular dioxygen to yield stable mu-oxodiiron(III) complexes. Crystal structure analyses are reported for each of these three mu-oxo compounds. With TPA, a symmetrical structure is obtained for a dicationic compound with the tripod coordinated in the kappa(4)N coordination mode. With FTPA, the compound is a neutral mu-oxodiiron(III) complex with a kappa(3)N coordination mode of the ligand. Oxygenation of the F(2)TPA complex gave a neutral unsymmetrical compound, the structure of which is reminiscent of that already found with the trifluorinated ligand. On reduction, all mu-oxodiiron(III) complexes revert to the starting iron(II) species. The oxygenation reaction parallels the well-known formation of mu-oxo derivatives from dioxygen in the chemistry of porphyrins reported almost three decades ago. The striking feature of the series of iron(II) precursors is the effect of the ligand on the kinetics of oxygenation of the complexes. Whereas the parent complex undergoes 90 % conversion over 40 h, the monofluorinated ligand provides a complex that has fully reacted after 30 h, whereas the reaction time for the complex with the difluorinated ligand is only 10 h. Analysis of the spectroscopic data reveals that formation of the mu-oxo complexes proceeds in two distinct reversible kinetic steps with k(1) approximately 10 k(2). For TPAFeCl(2) and FTPAFeCl(2) only small variations in the k(1) and k(2) values are observed. By contrast, F(2)TPAFeCl(2) exhibits k(1) and k(2) values that are ten times higher. These differences in kinetics are interpreted in the light of structural and electronic effects, especially the Lewis acidity at the metal center. Our results suggest coordination of dioxygen as an initial step in the process leading to formation of mu-oxodiiron(III) compounds, by contrast with an unlikely outer-sphere reduction of dioxygen, which generally occurs at negative potentials.