On the convergence rate improvement of a primal-dual splitting algorithm for solving monotone inclusion problems

We present two modified versions of the primal-dual splitting algorithm relying on forward–backward splitting proposed in V\(\tilde{\mathrm{u}}\) (Adv Comput Math 38(3):667–681, 2013) for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators involved we obtain for the sequences of iterates that approach the solution orders of convergence of \(\mathcal{{O}}(\frac{1}{n})\) and \(\mathcal{{O}}(\omega ^n)\), for \(\omega \in (0,1)\), respectively. The investigated primal-dual algorithms are fully decomposable, in the sense that the operators are processed individually at each iteration. We also discuss the modified algorithms in the context of convex optimization problems and present numerical experiments in image processing and pattern recognition in cluster analysis.     

Corelationship between local structure and water purifying ability of iron-containing waste glasses

A relationship between the structure and water purifying ability of waste glass prepared from household garbage and Fe₂O₃ was examined by ⁵⁷Fe-Mössbauer and induced coupled plasma (ICP) measurements. From the Debye temperature of waste glass, Fe^II proved to be loosely bound in the glass network as a network modifier. Dissolution amount of Fe^III into artificial drain can be controlled from 0.14 to 0.35 mg/l by changing the Fe₂O₃ content. It proved that chemical oxygen demand (COD) decreases in proportion to the content of Fe^III, indicating that iron causes decomposition of organic and phosphorus compounds.     

Electrical conductivity and local structure of lithium iron tungsten vanadate glass

A relationship between physical properties and local structure of 20Li₂O·10Fe₂O₃·xWO₃·(70–x)V₂O₅ glass, abbreviated as xLFWV glass (x?=?0???25 in mol%), was investigated by ⁵⁷Fe-Mössbauer spectroscopy, Fourier transform infrared spectroscopy (FT-IR), differential thermal analysis (DTA), leaching test using 20 vol% HCl and DC two- or four-probe method. ⁵⁷Fe-Mössbauer spectra of xLFWV glass showed an increase of quadrupole splitting (Δ) from 0.67 to 0.73_±0.02 mm s^???1 and a constant isomer shift (δ) of 0.39_±0.01 mm s^???1 with an increase of ‘x’ from 0 to 25. This suggests that Fe^IIIO₄ tetrahedra gradually increase their local distortion along with a substitution of WO₃ for V₂O₅. DTA of xLFWV glass showed an increase in glass transition temperature (T _g) from 252 to 298 $_{\pm 5}^{\circ}$ C with an increase of ‘x’. Composition dependency of T _g and Δ indicates that Fe^III atoms occupy substitutional sites of WO₆ octahedra as network former (NWF), since a large slope of 680 K (mm s^???1)^???1 was obtained in T _g ? Δ plot. Comparable electrical conductivities (σ) of 2.5 × 10^???6, 1.9 × 10^???6, 8.4 × 10^???7 and 2.9 × 10^???6 S cm^???1 obtained for xLFWV glasses with ‘x’ of 0, 10, 20 and 25, respectively increased to 2.4 × 10^???2, 2.4 × 10^???3, 3.5 × 10^???4 and 8.8 × 10^???5 S cm^???1 after annealing at 400 °C for 100 min. Smaller Δ values of 0.58 and 0.67_±0.02 mm s^???1 obtained in annealed xLFWV glasses with ‘x’ of 0 and 10, respectively indicate that structural relaxation occurs in VO₄ units of vanadate glass units, as had been observed in other vanadate glasses.     

Local structure and water cleaning ability of iron oxide nanoparticles prepared by hydro-thermal reaction

Nanoparticles (NPs) of Fe₃O₄ and γFe₂O₃ synthesized by hydrothermal reaction were characterized by X-ray diffractometry (XRD), ⁵⁷Fe-Mössbauer spectroscopy and field emission scanning electron microscopy (FE-SEM). A decrease in concentration of methylene blue (MB) aqueous solution due to bulk Fe⁰-NP γFe₂O₃ mixture with the mass ratio of 3:7 was measured by ultraviolet-visible light absorption spectroscopy (UV-Vis). The Mössbauer spectrum of NP Fe₃O₄ prepared from hydrothermal reaction was composed of two sextets with absorption area (A), isomer shift (δ) and internal magnetic field (H _int) of 56.3 %, 0.34_±0.03 mm s^???1 and 49.0_±0.30 T for tetrahedral (T _d) Fe^III, and 43.7 %, 0.66_±0.11 mm s^???1 and 44.0_±0.71 T for octahedral (O _h) Fe^II?+?III. The Fe^II/Fe^III ratio was determined to be 0.280 for NP Fe₃O₄, giving ‘x’ of 0.124 in Fe_3???xO_4. These results show that NP Fe₃O₄ prepared by hydrothermal reaction was not regular but nonstoichiometric Fe₃O₄. Consistent results were observed for XRD patterns of NP Fe_3???xO₄ indicating sharp intense peaks at 2Θ of 30.2, 35.7 and 43.3° with a large linewidth of 0.44°, yielding the crystallite size of 29–37 nm from the Scherrer’s equation. Iso-thermal annealing of NP Fe_3???xO₄ at 250 °C for 30 min resulted in the precipitation of NP γFe₂O₃ with δ of 0.33_±0.03 mm s^???1 and H _intof 46.4_±0.27 T due to magnetic tetrahedral Fe^III. The Debye temperature of NP Fe_3???xO₄ was respectively estimated to be 267_±5.45 K for Fe $^{\mathrm{III}}(T_{\mathrm{d}})$ and 282_±7.17 K for Fe $^{\mathrm{II+III}}(O_{\mathrm{h}})$ , both of which were smaller than that obtained for bulk Fe₃O₄ of 280_±4.15 K and 307_±5.70 K, indicating that the chemical environment of iron of NPs is less rigid than that of the bulk compounds. A leaching test using methylene blue (MB) and mixture of bulk Fe⁰-NP γFe₂O₃ (3:7) showed a remarkable decrease in MB concentration from 1.90 × 10^???2 to 9.49 × 10^???4 mM for 24 h with the first order rate constant (k _MB) of 2.1 × 10^???3 min^???1. This result verifies that MB decomposing ability is enhanced by using NP γFe₂O₃ compared with the k _MB of 1.1 × 10^???4 min^???1 previously obtained from the leaching test using MB and bulk mixture of Fe⁰???γFe₂O₃ (3:7).     

Mössbauer study of new vanadate glass with large charge-discharge capacity

Charge-discharge capacity and cyclicity of lithium ion battery (LIB) was evaluated in which 15Li₂O·10Fe₂O₃·xSnO₂·5P₂O₅·(70–x)V₂O₅ glass (x?=?0 and 20 in mol%, abbreviated as xLFSPV) was used as a cathode. A local structure of xLFSPV glass before and after charging was investigated by ⁵⁷Fe- and ¹¹⁹Sn-Mössbauer spectroscopies. ⁵⁷Fe-Mössbauer spectrum of xLFSPV glass with ‘x’ of 20 was composed of a doublet with isomer shift (δ) of 0.35_±0.02 mm s^???1 and quadrupole splitting (Δ) of 0.88_±0.03 mm s^???1 due to distorted Fe^IIIO₄ tetrahedra. ¹¹⁹Sn-Mössbauer spectrum of this glass consisted of a doublet with δ of 0.08_±0.01 and Δ of 0.52_±0.01 mms^???1 due to distorted Sn^VIO₆ octahedra. After discharging the battery from 4.5 to 1.0 V, larger δ of 0.40_±0.03 mm s^???1 and Δ of 0.94_±0.04 mm s^???1 were obtained, indicating that both iconicity of Fe-O bonds and local distortion of Fe^IIIO₄ tetrahedra were increased. On the contrary, identical δ of 0.09_±0.01 mm s^???1 and Δ of 0.50_±0.01 mm s^???1 were observed in the ¹¹⁹Sn-Mössbauer spectrum of 20LFSPV glass after the discharge, indicating that chemical environment of Sn^IVO₆ octahedra was not affected after the discharge. Charge-discharge curve of LIB containing 20LFSPV glass as a cathode active material recorded under the current density of 8.3 mA g^???1 (0.011 mA cm^???2) between 1.0 and 4.5 V showed a large initial charge capacity of 431.1 mAh g^???1 and discharge capacity of 382.3 mAh g^???1, respectively. These results indicate that 20LFSPV glass could be a new cathode active material for LIB.     

Comparative study of hydroxo-fluoro and hydroxo-sulphido mixed ligand complexes of aluminum(III) and gallium(III)

The mixed ligand complex formation had been studied in the aluminate-fluoride, gallate-fluoride, aluminate-sulphide and gallate-sulphide systems by spectrophotometric as well as potentiometric methods using glass and sulphide selective electrodes. The formation of the species Al(OH)₃F^? and Ga(OH)₂S^? has been demonstrated and the equilibrium constants have been determined. Similar interaction could not be detected in the aluminate-sulphide and gallate-fluoride systems.The differences in behaviour of the metal ions to the characteristically hard fluoride and soft sulphide ligands can be interpreted in that the Ga³⁺ ion may form complexes with charged soft ligands too, its behaviour then differing from that of the typically hard Al³⁺ ion.     

High-pressure NMR study of water exchange on magnetic resonance imaging contrast agents

Abstract

The knowledge of water exchange reaction mechanism in aqueous solutions of Gd³⁺ polyaminocarboxylates is important for the understanding of the relatively slow water exchange rates measured for these complexes. Variable ressure measurements show a change of mechanism from associatively activated on [Gd(H₂O)₈]³⁺ and [Gd(PDTA)(H₂O₂)₂]^? to probably limiting dissociative on the MRI contrast agents [Gd(DOTA)(H₂O)]^?, [Gd(DTPA)(H₂O)]^2? and [Gd(DTPA-BMA)(H₂O)].     

Redox interactions between structurally different alkylresorcinols and iron(III) in aqueous media: frozen-solution 57Fe Mössbauer spectroscopic studies,redox kinetics and quantum chemical evaluation of the alkylresorcinol reactivities

Iron(III)-containing aqueous solutions of 5-methylresorcinol (5-MR), 5-n-propylresorcinol (5-n-PR) and 4-n-hexylresorcinol (4-n-HR) at pH ~ 3 were studied by means of ⁵⁷Fe transmission Mössbauer spectroscopy. Kinetic considerations were applied to the redox reactions. Density Functional Theory (DFT) calculations were performed for the alkylresorcinol (AR) molecules and their non-alkylated analogue (resorcinol). Mössbauer spectra consisted of quadrupole doublets assigned to high-spin Fe(III) and Fe(II) species. From changes in their relative spectral areas, a gradual reduction of Fe(III) by all the ARs studied was observed. However, significant differences were found for the reduction rates among the ARs. The following series of the reduction rates was established by means of Mössbauer spectroscopy: 4-n-HR ? 5-MR > 5-n-PR, supplemented by rate constants calculated using a kinetic model. DFT calculations resulted in the following series: 4-n-HR ? 5-n-PR > 5-MR ? resorcinol (the latter is not oxidised under the conditions applied). The reversed order of the experimentally observed 5-MR and 5-n-PR oxidation rates may be explained in terms of their different kinetic parameters related to their structure.     

Influence of structural changes on the ion selectivities of magnesium ionophores based on malonic acid diamides

In an investigation of octamethylene bis(malonic acid diamides) and their selectivities for magnesium, it was found that presence of secondary amides within the particular ionophore played a considerable role in the enhancement of magnesium selectivity. Similar effects in other ionophores, i.e. tris(malonic acid diamides), were thus systematically looked at with the help of selectivity measurements with the hope of optimizing the number of secondary and tertiary amides so as to improve the magnesium selectivity. The syntheses of several investigated tris(malonic acid diamide) isologues are equally reported.Deceased in November 1992