On the solution of singular linear systems of algebraic equations by semiiterative methods

Summary For a square matrixT ^n,n , where (I–T) is possibly singular, we investigate the solution of the linear fixed point problemx=T x+c by applying semiiterative methods (SIM's) to the basic iterationx ₀ ⁿ ,x _k T c _k–1+c(k1). Such problems arise if one splits the coefficient matrix of a linear systemA x=b of algebraic equations according toA=M–N (M nonsingular) which leads tox=M ^–1 N x+M ^–1 bT x+c. Even ifx=T x+c is consistent there are cases where the basic iteration fails to converge, namely ifT possesses eigenvalues 1 with ||1, or if =1 is an eigenvalue ofT with nonlinear elementary divisors. In these cases — and also ifx=T x+c is incompatible — we derive necessary and sufficient conditions implying that a SIM tends to a vector which can be described in terms of the Drazin inverse of (I–T). We further give conditions under which is a solution or a least squares solution of (I–T)x=c.Research supported in part by the Alexander von Humboldt-Stiftung     

Dispersion effects of laminar flow and spray chamber volume in capillary electrophoresis-inductively coupled plasma-mass spectrometry: a numerical and experimental approach

Band broadening related to laminar flow and spray chamber dead volume is a potential problem in flow injection (FI)-inductively coupled plasma-mass spectrometry (ICP-MS). We studied these two dispersion effects with a sheath flow capillary electrophoresis (CE)-ICP-MS interface. A numerical model was used to simulate advection diffusion processes in the CE-capillary and dispersion in the spray chamber. Experimental results of FI with this CE-ICP-MS interface agree well with numerical modeling results. Dispersion due to laminar flow depends strongly on capillary diameter and analyte diffusion coefficient and to a lesser extent on laminar velocity and capillary length and typically amounts to one order of magnitude peak width increase. Three spray chambers of 5, 20 and 150 ml dead volume showed an increase in band broadening and peak tailing with increasing dead volume. The use of standard Scott-type spray chambers (>90 ml volume) increases peak widths by 5-10 s regardless of injection time. The use of a low dead volume spray chamber is recommended for experiments where resolution is critical. The modeling approach can be extended to the coupling of other flow injection techniques, like micro-LC and nano-LC with ICP-MS.     

Luteone,a twenty three carbon terpenoid from the dorid nudi branch Cadlina luteomarginata

The structure of luteone ($\text{1}$), a twenty three carbon terpenoid, has been solved by performing a single crystal x-ray analysis on a 3,4-dinitrophenylhydrazone derivative.     

Nuclear Techniques in the Elucidation of Chemical Structure

The paper offers three applications of nuclear methods in the research of chemical structure. First, progress in positron annihilation spectroscopy is illustrated by a positron beamline study, which obtained results that are not available through conventional experiments. The positron beam was used for the study of Langmuir-Blodgett (LB) films containing 4-58 layers of arachidic acid and its salts. These measurements have shown that this emerging technique is capable of characterizing even such elusive systems. Second, the potential of Mössbauer spectroscopy to answer current challenges of solid state chemistry are shown in a study on perovskites of recent interest. ¹⁵¹Eu Mössbauer spectroscopy was used to study the effect of Pr substitution in EuBa₂Cu₃O_7-. It was shown that the introduction of Pr into the rare earth site as well as into the Ba site results in the appearance of extra electrons both in the copper oxide planes and at the 4f shell of Eu cations. The observed effects were explained by the hole filling effect of Pr. Finally, a survey is presented on the recently developed techniques for nuclear resonant scattering of synchrotron radiation, an exciting and very rapidly developing extension to conventional Mössbauer spectroscopy. An interesting new result is that nuclear inelastic scattering experiments performed on solutions of ⁵⁷Fe complexes show contribution from vibrations rather than from diffusion to the inelastic spectra.     

EXTRARETINAL PHOTORECEPTION IN CHICKENS: ENTRAINMENT OF THE CIRCADIAN LOCOMOTOR ACTIVITY RHYTHM

Abstract— The Circadian locomotor activity rhythm of blinded chickens entrained to, or was synchron ized by, light in light dark cycles.     

Validation of the thermodynamic model of inorganic arsenic in non polluted river waters of the Basque country (Spain)

The thermodynamic model of inorganic arsenic was validated by comparing the predicted As(III) concentration with the experimentally determined one in several river waters samples of the Basque Country (Spain) collected in two sampling campaigns: spring and autumn 2000. This model takes into account the acid-base equilibria of As(III) and As(V) together with the redox equilibria between the H₃AsO₃ and H₃AsO₄ species. A correct prediction of As(III) concentration requires the knowledge of the total concentration of arsenic, pH, redox potential (referred to hydrogen electrode), and ionic strength values of the solution. The estimation of the activity coefficients of the arsenic species was performed by means of the Modified Bromley’s Methodology (MBM).In order to perform the experimental As(III) determination, an analytical method was implemented by using an ion exchange separation of As(III)/As(V) on a continuous FIA-IE-HG-AAS system. The total arsenic concentration was determined together with total concentration of the main alkaline or alkaline-earth metals and anions in the natural waters. Temperature compensated measurements of the pH and redox potentials were made in-situ at the sampling sites.For both seasonal campaigns, the agreement between predicted and experimental As(III) is really high for those samples belonging to non polluted river waters.     

Compressibility and Volume Effects of Mixing of 1-Propanol with Heavy Water

Speed of sound and density of 1-propanol + heavy water were measured in the whole concentration range at temperatures from 293 to 313 K. Isentropic compressibility was calculated from the Laplace formula. The partial molar volume of 1-propanol reaches a minimum at the mole fraction of 1-propanol x ₁ 0.03. At the same concentration, the compressibility isotherms intersect one another. These features of the investigated system are similar to those of 1-propanol + H₂O, that points to essential similarity of the two mixtures. A clathrate-like structure was suggested to explain the experimental results for dilute solutions of the alcohol. Somewhat more pronounced hydrophobic hydration in D₂O than in H₂O is manifested by an effect similar to that resulting from the elongation of the alcohol molecule.     

Cinnamaldehyde hydrogenation using ruthenium-tin catalyst type

Bimetallic ruthenium-tin catalysts were prepared using the sol-gel method and the method of carrier impregnation. Two different procedures were used for their reduction — reduction in hydrogen atmosphere under an increased temperature, and reduction using an aqueous solution of sodium borohydride. Hydrogenation of 3-phenylpropenal (cinnamaldehyde) in tetrahydrofuran at 433 K and the total pressure 7 MPa was used as the model reaction for comparing the catalytic properties of the prepared catalysts. It was demonstrated that a tin addition notably affected catalytic properties of ruthenium in the sense of a selectivity increment related to the production of an unsaturated alcohol.