Fast Algorithms for Centro-Symmetric and Centro-Skewsymmetric Toeplitz-Plus-Hankel Matrices

Subject of the paper are centro-symmetric and centro-skewsymmetric Toeplitz-plus-Hankel matrices with the property that all central submatrices are nonsingular. Fast algorithms are presented that solve an n×n system of equations with O(n ²) operations in sequential and O(n) operations in parallel processing and compute the ZW-factorization with the same computational complexity. These algorithms are more efficient than existing algorithms because they fully exploit the symmetry properties of the matrices.     

Fast inversion algorithms of Toeplitz-plus-Hankel matrices

Summary The paper deals with the problems of fast inversion of matricesA=T+H, whereT is Toeplitz andH is Hankel. Several algorithms are presented and compared, among them algorithms working for arbitrary strongly nonsingular matricesA=T+H.     

Baryon resonance components in the deuteron

A non-relativistic coupled channel calculation of the structure of the deuteron is presented with NN¹ configurations in addition to the usual (NN) S- and D-state components. The additional baryon resonance degrees of freedom are included by means of a one-pion exchange potential model; the nucleon-nucleon interactions are treated with conventional phenomenological potentials which contain a hard core. This core obviates the necessity for additional cutoff parameters for the singular NN¹ potentials. All possible NN¹ states of the ten currently “well-established” N¹ resonances have been calculated using a renormalized Reid hard core potential and several NN¹ amplitudes are found in the 0.1–0.3% range. Some of these components are rather large at high momenta and thus may be observable in high momentum transfer processes.     

Zur Spektralanalyse von Siliciumcarbid

Zusammenfassung Aus der Diskussion der Grundlagen einer spektrographischen Siliciumearbidanalyse und deren Ergebnissen folgt die Überlegenheit gegenüber der chemischen Analyse bei der relativen Gehaltsbestimmung verunreinigender Fremdelemente (Al, Fe, Ti und Mg), die bei einfacher Methode mit einem mittleren Fehler von 7 bis 15% durchgeführt werden kann. Die absolute Gehaltsangabe ist größenordnungsmäßig möglich.Die Analysenergebnisse an zahlreichen SiC-Proben zeigen eine deutliche Abhängigkeit der Eigenschaften vom Al-Gehalt, die durch extrem hohe bzw. niedrige Werte von Fe und Ti beeinflußt werden kann.

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Summary The discussion of the fundamentals of a spectrographic analysis of silicon carbide and their results shows its superiority as compared with chemical analysis in the relative determination of the content of contaminating foreign elements (Al, Fe, Ti, Mg). This analysis can be conducted by a simple method with a mean error of 7 to 15%. It is possible to state the absolute content in order of size.The analytical results in many samples of SiC show a distinct dependence of the properties on the Al-content, which may be influenced by extremely high or low values of iron and titanium.

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Résumé De la discussion des principes de base d'une méthode d'analyse spectrographique de carbure de silicium résultel a supériorité de cette méthode par rapport à l'analyse chimique pour le dosage relatif des éléments étrangers (Al, Fe, Ti, Mg); ils sont dosés par une méthode simple avec une précision moyenne de 7 à 15%. On peut aussi déterminer la valeur absolue de leur concentration, au moins en ordre de grandeur.Les résultats d'analyse de nombreux échantillons de SiC révèlent une influence nette, sur leurs propriétés, de la concentration en Al qui peut être modifiée par de très fortes (ou de très faibles) teneurs en fer ou titane.

     

Über Addukte und Salze von Schwefelchloriden mit AlCl3

Adducts and Salts Formed by Sulphurchlorides with AlCl₃ The instability of the adduct 2 S₂Cl₂ · AlCl₃ is proven. S₂Cl₂ · AlCl₃ and S₂Cl₂ · 2 AlCl₃ reported in the literature could not be found under proper conditions, their formation seems improbable. The product 2 SCl₄ · 3 AlCl₃, obtained by the reaction of [SCl₃]⁺[AlCl₄]^? with elementary sulphur, is characterized as a double salt [SCl₃]₂+[AlCl₄]^? [Al₂Cl₇]^?. The [Al₂Cl₇]^? anion is also found as an intermediate during the thermal decomposition of [SCl₃]⁺[AlCl₄]^? and when metallic aluminium reacts directly with S₂Cl₂. For SCl₂ · AlCl₃, the ionic character with a chlorsulfenium cation [SCl]⁺ is proven spectroscopically.