Theorems of Stein-Rosenberg type. III. The singular case

In the theory of iterative methods, the classical Stein-Rosenberg theorem can be viewed as giving the simultaneous convergence (or divergence) of the extrapolated Jacobi (JOR) matrix J_ω and the successive overrelaxation (SOR) matrix

, in the case when the Jacobi matrix J₁ is nonnegative. As has been established recently by Buoni and Varga, necessary and sufficient conditions for the simultaneous convergence (or divergence) of J_ω and

have been established which do not depend on the assumption that J₁ is nonnegative. Our aim here is to extend these results to the singular case, using the notion of semiconvergence. In particular, for a real singular matrix A with nonpositive off-diagonal entries, we find conditions (Theorem 3.4) which imply that J_ω and

simultaneously semiconverge for all ω in the real interval [0,1).     

Dichloro and alkylchloro gallium derivatives of dichalcogenoimidodiphosphinate ligands: isolation of a spirogallium cation

Dichloro and chloromethyl Ga(III) complexes of general formulae [XClGa-eta2-{R2P(E)NP(E'R'2-E,E'}](X = Cl, R, R'= Ph, E, E'= O (1), S (2), Se (3); R = Ph, R'= OEt, E = O, E'= S (4); R = Me, R'= Ph, E, E'= S (5) and X = Me, E, E'= O (6), S (7), Se (8)) were synthesised by either metathesis reactions between GaCl3 and the potassium salt of the ligand (X = Cl) or by methane eliminations from in situ prepared GaMe2Cl and the protonated ligands LH (X = Me). Redistribution reaction of (3) in either CDCl3 or THF afforded the solvent-free tetracoordinate gallium spirocycle cation [Ga-{eta2-{Ph2P(Se)NP(Se)Ph2-Se,Se'})2]+ (9+). The molecular structures of complexes 2, 4, 5, 7 and 9(+) show non-planar gallacycle rings.     

Correlation between Small-Angle X-ray Scattering spectra and apparent diffusion coefficients in the study of structure and interaction of sodium taurodeoxycholate micelles

Small-Angle X-ray Scattering (SAXS) and Dynamic Light Scattering (DLS) measurements were carried out on aqueous micellar solutions of the ionic biological detergent sodium taurodeoxycholate (NaTDC). Apparent diffusion coefficients (D(app)) and SAXS spectra of NaTDC 0.1 M solutions at different ionic strengths (0.1-0.3 M NaCl) were reported. A comparative analysis of SAXS spectra and D(app) data was performed to infer information on particle structure and interaction potential. Uniform particles with a spherical, an oblate, and a prolate symmetry were used to model the micelles in the data interpretation. A hard-core interaction shell of suitable thickness and a screened Coulomb potential of the electric double layer (EDL potential) were alternatively used to represent the long-range repulsive tail of the interaction potential. The Percus Yevick and the Rescaled Mean Spherical Approximation were applied. To compare the data of the two techniques, for each sample, a D(app) was calculated from the SAXS best-fitting geometrical parameters and interparticle structure factor of the micelles. Hence, a fitting procedure involving both the scattering and D(app) data was performed. The interpretation of SAXS spectra does not allow the discrimination between the oblate and the prolate symmetries of the aggregates. On the other hand, the comparison of calculated and experimental D(app) values indicates that the prolate ellipsoid is better suited to represent the micelle shape. Moreover, the agreement between calculated and experimental D(app) values is sensitively better at the lowest NaCl concentration when the EDL potential is used. A rodlike micellar growth and a progressive screening of the electrostatic interactions is testified by the trends of best-fitting parameters as a function of the added electrolyte.     

Fluorescence study of the interaction between metal ions and methyl methacrylate–methacrylic acid copolymers in aqueous solutions: thallium(I), calcium(II), and terbium(III)

 The binding of the cations thallium(I), calcium(II) and terbium(III) to methyl methacrylate– methacrylic acid copolymers with different fractions of acid groups (x) has been studied in aqueous solution at various pH values using the fluorescence of covalently bonded 9-vinyl anthracene as a probe. In all cases, the extent of binding increases as a function of the charge of the polymer with either increasing fraction of carboxylic acids or of pH. However, differences are observed in the behavior of the three cations. With Tl(I), quenching of the anthracene group fluorescence is observed, indicating that the thallium(I) approaches the probe and suggesting that the alkylanthracene is probably in a relatively polar region. Binding constants have been determined from anthracene quenching data and from studies with the fluo-rescent-probe sodium pyrenetetra-sulfonate. Good agreement is obtained between the two methods, and values for the binding constants increase from 250 to 950 M^-1 as x increases from 0.39 to 1. It is suggested that the cation is held in the polyelectrolyte domain, partly by Debye–Hückel effects and partly by more specific interactions. Stronger binding is found with calcium(II) and terbium(III), and in this case increases in fluorescence intensity are observed on complexation due to the anthracene group being in a more hydrophobic region, probably as a result of conformational changes in the polymer chain. In the former case the stoichiometry of the interaction was determined from the fluorescence data to involve two carboxylate groups bound per calcium. Association constants were found using murexide as an indicator of free calcium to vary from 8400 to 37 000 M^-1 as x increases from 0.39 to 1. It is suggested that in this case specific calcium(II)–carboxylate interactions contribute to the binding. With terbium(III), a greater increase in the probe fluorescence intensity was observed than with calcium, and it is suggested that the interaction with the polymer is even stronger, leading to a more pronounced conformational change in the polymer. It is proposed that the terbium(III) interacts with six carboxylic groups on the polymer chain, with three being coordinated and three attracted by electrostatic interactions. Received: 10 June 1997 Accepted: 24 October 1997     

Effect of ionic interactions on the oxidation of Fe(II) with H2O2 in aqueous solutions

The oxidation of Fe(II) with H₂O₂ has been measured in NaCl and NaClO₄ solutions as a function of pH, temperature T (K) and ionic strength (M, mol-L^–1). The rate constants, k (M^–1-sec^–1), d[Fe(II)]/DT=-k[Fe(II)][₂O₂]at pH=6.5 have been fitted to equations of the formlog k = log k₀+ AI ^1/2+BI+CI ^1/2/T Where log k₀=15.53-3425/T in water; A=–2.3, –1.35; B=0.334, 0.180; and C=391, 235, respectively, for NaCl (=0.09) and NaClO₄ ( =0.08). Measurements made in NaCl solutions with added anions yield rates in the order B(OH) ₄ ^– >HCO ₃ ^– >ClO ₄ ^– >Cl^–>NO ₃ ^– >SO ₄ ^2– and are attributed to the relative strength of the interactions of Fe²⁺ or FeOH⁺ with these anions. The FeB(OH) ₄ ⁺ species is more reactive while the FeCO ₃ ⁰ , FeCl⁺, FeNO ₃ ⁺ and FeSO ₄ ⁰ species are less reactive than the FeOH⁺ ion pair. The general trend is similar to our earlier studies of the oxidation of Fe(II) with O₂ except for B(OH) ₄ ^– . The effect of pH on the logk was found to be a quadratic function of the concentration of H⁺ or OH^– from pH=4 to 8. These results have been attributed to the different rate constants for Fe²⁺ (k₀) and FeOH⁺ (k₁) which are related to the measured k by, k=k_0Fe + k_1FeOH, where _i is the molar fraction of species i. The rates increase due to the greater reactivity of FeOH⁺ compared to Fe²⁺. k₀ is independent of composition and ionic strength but k₁ is a function of ionic strength and composition due to the interactions of FeOH⁺ with various anions.     

THE INTERACTION OF THE EXCITED STATES OF SAFRANINE T WITH ALIPHATIC AMINES IN ORGANIC SOLVENTS

Abstract—
The reactions of the excited states of safranine T with aliphatic amines have been studied in methanol and acetonitrile. Quenching of the singlet and triplet states occurs by different mechanisms. Whereas the former excited state is quenched by a charge-transfer mechanism, the triplet state is quenched through proton transfer from the excited dye to the amine. This process leads to the unprotonated form of the dye in the triplet state, which is later quenched by amines to form the corresponding semireduced species. The monoprotonated triplet also undergoes self-quenching in both solvents (k = 1.2 × 10⁸ M ^-1 s^-1).     

Electronic structure of A- and B-site doped lanthanum manganites: a combined X-ray spectroscopic study

The electronic properties of a series of colossal magnetoresistance (CMR) compounds, namely LaMnO3, La(1-x)Ba(x)(MnO3 (0.2 < or = x < or = 0.55), La(0.76)Ba(0.24)Mn(0.84)Co(0.16)O3, and La(0.76)Ba(0.24)Mn(0.78)Ni(0.22)O3, have been investigated in a detailed spectroscopic study. A combination of X-ray photoelectron spectroscopy (XPS), X-ray emission spectroscopy (XES), X-ray absorption spectroscopy (XAS), and resonant inelastic X-ray scattering (RIXS) was used to reveal a detailed picture of the electronic structure in the presence of Ba, Co, and Ni doping in different concentrations. The results are compared with available theory. The valence band of La(1-x)()Ba(x)MnO3 (0 < or = x < or = 0.55) is dominated by La 5p, Mn 3d, and O 2p states, and strong hybridization between Mn 3d and O 2p states is present over the whole range of Ba concentrations. Co-doping at the Mn site leads to an increased occupancy of the e(g) states near the Fermi energy and an increase in the XPS valence band intensity between 0.5 and 5 eV, whereas the Ni-doped sample shows a lower density of occupied states near the Fermi energy. The Ni d states are located in a band spanning the energy range of 1.5-5 eV. XAS spectra indicate that the hole doping leads to mixed Mn 3d-O 2p states. Furthermore, RIXS at the Mn L edge has been used to probe d-d transitions and charge-transfer excitations in La(1-x)Ba(x)MnO3.     

Membrane electroporation and electromechanical deformation of vesicles and cells

Analysis of the reduced turbidity (delta T-/T0) and absorbance (delta A-/A0) relaxations of unilamellar lipid vesicles, doped with the diphenylhexatrienyl-phosphatidylcholine (beta-DPH pPC) lipids in high-voltage rectangular electrical field pulses, demonstrates that the major part of the turbidity and absorbance dichroism is caused by vesicle elongation under electric Maxwell stress. The kinetics of this electrochemomechanical shape deformation (time constants 0.1 < or = tau/microsecond < or = 3) is determined both by the entrance of water and ions into the bulk membrane phase to form local electropores, and by the faster processes of membrane stretching and smoothing of thermal undulations. Moreover, the absorbance dichroism indicates local displacements of the chromophore relative to the membrane normal in the field. The slightly slower relaxations of the chemical turbidity (delta T+/T0) and absorbance (delta A+/A0) modes are both associated with the entrance of solvent into the interface membrane/medium, caused by the alignment of the bipolar lipid head groups in one of the leaflets at the pole caps of the vesicle bilayer. In addition, (delta T+/T0) indicates changes in vesicle shape and volume. The results for lipid vesicles provide guidelines for the analysis of electroporative deformations of biological cells.     

Evaluation of the surface tension measurement of axisymmetric drop shape analysis (ADSA) using a shape parameter

A quantitative criterion called “shape parameter” to evaluate the quality of surface tension measurement of Axisymmetric Drop Shape Analysis (ADSA) is presented. ADSA is a powerful technique for the measurement of interfacial tensions and contact angles of pendant drops, sessile drops, and bubbles. Despite the general success of ADSA, deficient results may be obtained for drops close to spherical shape. Therefore, the “shape parameter” was used to determine the range of drop shapes in which ADSA succeeds or fails. The “shape parameter” is a dimensionless parameter that expresses quantitatively the difference in shape between a given experimental profile and an inscribed circle. The surface tension measurements of ADSA were evaluated for both pendant drop and constrained sessile drop configurations using the shape parameter. Different shapes of the pendant drop were studied using different sizes and materials of holders. For each drop configuration, a “critical shape parameter” was defined based on the minimum value of the shape parameter that guarantees an error of less than ±0.1 mJ/m². Furthermore, the effects of the type of liquid and constellation on the “critical shape parameter” were studied.     

Re4(CO)12[μ3-InRe(CO)5]4 und Re2(CO)8[μ-InRe(CO)5]2-cluster aus dem reaktionssystem In/Re2(CO)10 in xylol

The thermally stable solids Re₂(CO)₈[μ-InRe(CO)₅]₂ and Re₄(CO)₁₂[μ₃-InRe(CO)₅]₄ could be obtained by treatment of In with Re₂(CO)₁₀ in a bomb tube. A mechanism of the formation of the latter cluster from the first one is proposed. Compared with Re₂(CO)₈[μ-InRe(CO)₅]₂, Re₄(CO)₁₂[μ₃_InRe(CO)₅]₄ shows in polar solvents an unusual high stability, which can be explained by the higher coordination number of In with rhenium carbonyl ligands. Re₄(CO)₁₂-[μ₃-InRe(CO)₅]₄ dissolves monomerically in acetone, where as Re₂(CO)₈[μ-InRe(CO)₅]₂ dissociates yielding Re(CO)₅^? anions. Single-crystal X-ray analyses of Re₄(CO)₁₂[μ₃-InRe(CO)₅]₄ establish the metal skeleton. The central molecular fragment Re₄(CO)₁₂ contains a tetrahedral arrangement of four bonded Re atoms [ReRe 302.8 (5) pm]. The triangles of this fragment are capped with a μ₃-InRe(CO)₅ group each [InRe(terminal) 273.5 (7) pm; InRe (polyhedral) 281.8 (7) pm]. The bridging type of In atoms with the Re₄ tetrahedron and the metal skeleton was realized for the first time. By treating Re₄(CO)₁₂[μ₃-InRe(CO)₅]₄ with Br₂ the existence of Re(CO)₅ ligands could be proved by isolating BrRe(CO)₅.