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     

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.     

The fixed point property in ordered sets of width two

We consider the fixed point property (FPP) in an ordered set of width two (every antichain contains at most two elements). The necessary condition of the FPP and a number of equivalent conditions to the FPP in such sets is established. The product theorem is proved, as well.     

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.     

Electron-stimulated desorption from ionic crystal surfaces

Inelastic interactions of electrons with surfaces of ionic crystals result in emission of various particles such as ions, atoms and molecules. We will review such electron-stimulated desorption processes for the particular class of ionic crystals, namely for alkali halides. In this case, a dominant fraction of the emission is in the form of halogen and alkali atoms characterized by a thermal (Maxwellian) spectrum of translational energies. For several alkali halides (potassium and rubidium chlorides, bromides, and iodides), however, a significant part of the halogen atoms is ejected with nonthermal energies, i.e. energies of the order of 0.1 eV. The results of recent systematic studies of angular-resolved kinetic energy distributions of the emitted particles will be reported and current views on the electronic mechanisms of desorption will be described. In particular, it will be shown that the ESD mechanism can be understood in terms of the model involving a surface localisation of the so called “hot-holes” created by electron bombardment of alkali halides. A role of hot holes in ESD processes will further be discussed in relation to very recent experimental results obtained for the KBr crystals doped with In impurities which act as efficient hole traps.     

Microsolvation of the [Ni(acac)(tmen)]+ complex

Microsolvation of the [Ni(acac)(tmen)]⁺ complex by a series of aliphatic n-alcohols (Solv) has been studied in ClCH₂CH₂Cl solutions by spectrophotometry. Based on the changes in the electronic spectrum of the afore-mentioned complex, observed under the influence of any alcohol, the equilibrium constants for the formation of the [Ni(acac)(tmen)Solv]⁺ and [Ni(acac)(tmen)Solv₂]⁺ species have been computed according to the algorithm presented in this work. It was found that, in all the systems studied, the stability of five-coordinated [Ni(acac)(tmen)Solv]⁺ is higher than that of octahedral [Ni(acac)(tmen)Solv₂]⁺. The resulting values are discussed in terms of the Lewis basicity of alcohols.     

Formation of the radical-cation of monomer in the photoinduced polymerization of isobutylene in the presence of SnCl4

Spectra of isobutylene with SnCl₄ were studied at the temperature of 113°K in the dark and under illumination. Radical-cations of isobutylene are formed by irradiation of the isobutylene–SnCl₄ mixture in n-heptane substantially more slowly than in the isobutylene–TiCl₄ mixture. Polymerization of isobutylene occurs after increasing the temperature up to the melting point of this mixture. The yield of polymer depends on the duration of preirradiation, while the molecular weight of polyisobutylene (M _η) does not depend on the preirradiation of reaction mixture.     

The synthesis of 3,6-diamino-2,3,4,6-tetradeoxy-dl-threo-hexopyranose derivatives,substrates for the synthesis of negamycin

Three synthetic routes to derivatives of 3,6 - diamino - 2,3,4,6 - tetradeoxy - DL - threo - hexopyranose were investigated. Addition of sodium azide in acetic acid to 6 - phthalimido - 5,6 - dihydro - 2 - pyrone gave 4-azido compound (7) of the erythro configuration. From methyl 2,4 - dideoxy - β -dl- erythro - hexopyranoside threo 4 - phthalimido - 6 - phthalimidomethyl - tetrahydro - 2 - pyrone (17) was obtained in three steps in low overall yield. Addition of sodium azide in acetic acid to butyl 6 - oxo - 2 - hydroxy - hex - 4 - enoate followed by methylation, amonolysis of the ester group, and reduction gave methyl 3,6 - diacetamido - 2,3,4,6 - tetradeoxy - α - DL - threo - hexopyranoside (26).     

Electrochemical studies of Tl(I) crown-ether complexes in nonaqueous media

Summary Complexation equilibria of the Tl(I) ion with 18-crown-6 and dibenzo-18-crown-6 were studied polarographically in 10 nonaqueous solvents. The stability of the complexes is strongly influenced by the nature of solvents and varies with their Lewis basicities. It has been found that the logK _s value (K _s is the stability constant of the complex) can be well described by empirical relation logK _s=a DN+b, whereDN stands for the Gutmann donor number anda andb mark the regression coefficient. Addition of the second explanatory parameter, the acceptor number, is not statistically significant. This result is in agreement with the predominant role of Tl(I) ion solvation.

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Elektrochemische Untersuchungen von Tl(I)-Kronenetherkomplexen in nichtwäßrigen Medien

Zusammenfassung Es wurden die Komplexierungsgleichgewichte des Tl(I)-Ions mit 18-Krone-6 und Dibenzo-18-krone-6 polarographisch in 10 nichtwäßrigen Lösungsmitteln untersucht. Die Stabilität der Komplexe wird sehr stark vom Solvens beeinflußt, wobei eine starke Abhängigkeit von der Lewis-Basizität beobachtet wird. Es wurde festgestellt, daß die logK _s-Werte (K _s ist die Komplexstabilitätskonstante) gut mit der empirischen Beziehung logK _s=a DN+b beschrieben werden können, wobeiDN die Gutmann'sche Donorzahl unda undb die Regressionskonstanten bedeuten. Hinzunahme der Akzeptorzahl als zweiten Parameter bleibt statistisch insignifikant. Dieses Ergebnis stimmt mit dem dominierenden Einfluß der Tl(I)-Ionensolvatation überein.