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).     

An improved method for assay of vitamin C in fish feed and tissues

Summary A method was devised to assay four forms of vitamin C: L-ascorbic acid (AA), dehydroascorbic acid (DHA), ascorbate-2-mono- and polyphosphate (AMP, APP), as well as ascorbate-2-monosulphate (AMS), in sample series of different fish tissues and feed. Direct and indirect detection were combined. Sample extractions were carried out with 0.2 mol L⁻¹ sodium acetate buffer (pH 4.8) and extracts were deproteinized after different chemical or enzymatic reactions, with perchloric acid. The DHA was reduced to AA with dithioerythritol (DTE). Ascorbate oxidase enzyme was used for the detection of background and an acidic phosphatase enzyme for the hydrolysis of different phosphate esters. Ascorbate-2-sulphate was detected directly with help of coinjection of the compound. Chromatographic analysis was carried out with a single column isocratic reverse phase method. The mobile phase was an aqueous buffer of 0.04 M sodium-acetate, 0.05 mM EDTA, 0.5 mM tetrabutylammonium dihydrogen phosphate (TBA) adjusted to pH 3.76 with 85% H₃PO₄ and with 24 mL methanol added to 1000 mL. C-18 columns were used with 0.6 mL min⁻¹ flow rate at 23°C. The vitamin C forms were detected by UV absorption at 250 nm. The determination limit was 1.0–5.0 μg g⁻¹ in AA equivalent. The standard deviations were between 1–6% and depended on the concentrations of vitamin C forms and tissues. Recoveries were between 90–96% in samples. Presented at: Balaton Symposium on High-Performance Separation Methods, Siófok, Hungary, September 3–5, 1997     

Adsorption of sodium alkyl sulfate homologues at the air/solution interface

Experimental results are presented on the adsorption of sodium alkyl sulfate homologues (nC = 8-14) at the air/solution interface. The adsorption isotherms calculated from equilibrium surface-tension vs concentration data and the critical micelle concentration change regularly with the length of the alkyl chain; the odd/even effect was not observed. The isotherms were analyzed using a model-independent approach. The analysis indicates that the total driving force of adsorption reaches a plateau value and becomes constant in the function of the adsorbed amount in the case of each homologue. With the use of different electrostatic models, it was demonstrated that this behavior is consistent with a saturation-type hydrophobic driving-force contribution, which can be interpreted by the development of a liquidlike alkane environment in the adsorbed layer above a "critical" adsorbed amount.     

Synthesis, ring transformations, IR-, NMR and DFT study of heterocycles with two ferrocenyl units

Cyclization of 1,5-bis(ferrocenylmethylidene)thiocarbonohydrazide with DMAD afforded diastereomeric dimethyl-thiazole-4,5-dicarboxylates. The cis-isomer undergoes ring opening and recyclization to a thiazolone derivative. A further thiazolone was obtained from this precursor with ethyl chloroacetate employing a bifunctional organocatalyst. Due to its propensity to dehydrogenation evidenced by DFT calculations, the studied thiocarbonohydrazide underwent oxidative cyclizations under different conditions to yield a 1,3,4-thiadiazole and a 1,2,4-triazole derivative, respectively. Thermal isomerisation of 1,3,4-thiadiazole into 1,2,4-triazole was also observed. The DMAD-mediated cyclizations of the S-metylated thiocarbonohydrazide and the 1,5-bis(ferrocenylmethylideneamino)guanidine gave 1,2,4-triazole derivatives and a 4-pyrimidone, respectively. The structure of the new compounds was established by IR and NMR spectroscopy, including HMQC, HMBC and DEPT measurements. The solid state structure of a triazole was revealed by single crystal X-ray analysis.     

Adsorption of sugar surfactants at the air/water interface

The adsorption isotherms of n-decyl-β-D-glucoside (β-C(10)G(1)) as well as various n-alkyl-β-D-maltosides (β-C(n)G(2)) with n=8, 10, 12 and 14 were determined from surface tension measurements. Based on the analysis of the adsorption isotherms, the total free energy change of adsorption was determined and a novel method was proposed to determine the maximum adsorbed amount of surfactant. It can be concluded that the driving force for adsorption first increases with increasing adsorbed amount of the sugar surfactants and then levels off in a plateau. This peculiar behaviour is interpreted as formation of a thin liquid-like alkane film of overlapping alkyl chains at the air/water interface once a certain adsorbed amount is exceeded. The driving force of adsorption depends on the alkyl chain length only and is not affected by the type of the head group. The hydrophobic contribution to the standard free energy change of adsorption was compared with the values of sodium alkylsulfate and alkyltrimethylammonium bromide surfactants. This comparison reveals that the hydrophobic driving force of adsorption is the largest for the sodium alkylsulfates, whereas it is the same for the sugar surfactants and the alkyltrimethylammonium bromides.     

Influence of salt and rinsing protocol on the structure of PAH/PSS polyelectrolyte multilayers

A quartz crystal microbalance (QCM) and dual polarization interferometry (DPI) have been utilized to study how the structure of poly(allylamine hydrochloride) (PAH)/poly(styrene sulfonate) (PSS) multilayers is affected by the rinsing method (i.e., the termination of polyelectrolyte adsorption). The effect of the type of counterions used in the deposition solution was also investigated, and the polyelectrolyte multilayers were formed in a 0.5 M electrolyte solution (NaCl and KBr). From the measurements, it was observed that thicker layers were obtained when using KBr in the deposition solution than when using NaCl. Three different rinsing protocols have been studied: (i) the same electrolyte solution as used during multilayer formation, (ii) pure water, and (iii) first a salt solution (0.5 M) and then pure water. When the multilayer with PAH as the outermost layer was exposed to pure water, an interesting phenomenon was discovered: a large change in the energy dissipation was measured with the QCM. This could be attributed to the swelling of the layer, and from both QCM and DPI it is obvious that only the outermost PAH layer swells (to a thickness of 25-30 nm) because of a decrease in ionic strength and hence an increase in intra- and interchain repulsion, whereas the underlying layers retain a very rigid and compact structure with a low water content. Interestingly, the outermost PAH layer seems to obtain very similar thicknesses in water independent of the electrolyte used for the multilayer buildup. Another interesting aspect was that the measured thickness with the DPI evaluated by a single-layer model did not correlate with the estimated thickness from the model calculations performed on the QCM-D data. Thus, we applied a two-layer model to evaluate the DPI data and the results were in excellent agreement with the QCM-D results. To our knowledge, this evaluation of DPI data has not been done previously.     

On the alcohol inhibition of the reacting BZ system

The effect of aliphatic alcohols on the reacting BZ system has been studied and the mechanism of alcohol inhibition interpreted.

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Potentiometric detection in flow analysis

Special aspects of ion-selective electrodes relevant to applications in flow-through systems are discussed. The predominant role of the dynamic response characteristics of the sensor, especially in flow-injection analysis, is emphasized. Indirectly, these characteristics can affect the linear response range, the detection limit and the selectivity properties of the sensors. As examples, flow-injection methods are described for the determination of fluoride in rain-water samples and of potassium ion activity in blood sera.     

The Ru(dipy)32+-Bromate-Malonic acid oscillating system

The Ru(dipy) ₃ ²⁺ -bromate-malonic acid oscillating system was in vestigated. It has been established that at early stages of the reaction the period of oscillation is about 20 sec and the potential change is about 170 mV; chloride at concentrations hiherg than 10^–3M is an inhibitor. The rates of both heat evolution and formation of bromomalonic acid are periodic. The activation energy of the oscillating (E) is 16.2 kcal mol^–1. Ru(dipy) ₃ ²⁺ -- . , 20 , 170 ; , - 10^–3 M, . . (E) 16,2 /.