Hermitian quadratic eigenvalue problems of restricted rank

We consider a quadratic eigenvalue problem such that the second order term is a Hermitian matrix of rank r, the linear term is the identity matrix, and the constant term is an arbitrary Hermitian matrix . Of the n+r solutions that this problem admits, we show at least n-r to be real and located in specific intervals defined by the eigenvalues of A, whence at most 2r are nonreal occuring in possibly repeated conjugate pairs.     

CuAl2Cl8. Darstellung und Kristallstruktur

CuAl₂Cl₈. Preparation and Crystal Structure. Crystals of CuAl₂Cl₈ have been prepared. Their remission spectrum agrees with that of gaseous CuAl₂Cl₈. The crystal structure (P2₁/c;a = 6.614, b = 7.376, c = 12.319 Å; β = 94.11°) shows a molecular lattice with Cu in square planar coordination, which is completed to a stretched octahedron (as in solid CuCl₂) by two Cl atoms from neighbour molecules. Al has tetrahedral coordination.     

Ungewöhnliche Bildung und Struktur eines O‐Sulfinato‐Zinkkomplexes

Unusual Formation and Structure of a O‐Sulfinato Zinc Complex Whereas the reaction between hydrotris[(N‐xylyl)‐thioimidazolyl]borato‐zinc perchlorate ([ L· Zn‐OClO₃]) and ethanethiolate under an inert atmosphere leads to the thiolate complex [ L· Zn‐SC₂H₅], the same reaction in air produces the sulfinato complex [ L· Zn‐O‐S(O)‐C₂H₅] ( 1 ). 1 is the first fully characterized sulfinato‐zinc complex. Its structure determination has confirmed the unusual coordination of the sulfinato ligand via one of its oxygen atoms.     

Solid-phase synthesis of imidazo[4,5-b]pyridin-2-ones and related urea derivatives by cyclative cleavage of a carbamate linkage

A solid-phase synthesis of substituted cyclic urea derivatives as potential heterocyclic library scaffolds is described. 2-Amino-3-nitropyridine is attached to Wang resin via a carbamate linkage. Reduction of the nitro group was achieved with SnCl(2).2H(2)O. Reductive alkylation with a range of substituted benzaldehydes followed by cyclative cleavage afforded a small library of 3-substituted imidazo[4,5-b]pyridine-2-ones in 33-45% yield and 59-88% purity. Subsequently, this methodology was applied to the synthesis of 3-substituted imidazo[4,5-f]quinolin-2-ones.     

Dediazoniations of Arenediazonium Ions in Homogeneous Solutions. Part XV. Products of dediazoniation of p-chlorobenzenediazonium tetrafluoroborate in weakly alkaline aqueous solutions

The products of decomposition of solutions of p-chlorobenzenediazonium tetrafluoroborate in aqueous buffer solutions (pH 9.0–10.3; ionic strength 0.1–0.5) at 20.0° have been analyzed quantitatively. Up to eleven low molecular weight compounds could be identified besides the major product, the complex polymeric diazo tar. The distribution of products is influenced by trace amounts of oxygen as well as by p-chlorophenol and the radical trapping reagent iodoacetic acid. Mechanisms of formation of the products are discussed.     

Synthese und Molekülstrukturen von N‐substituierten Diethylgallium‐2‐pyridylmethylamiden

Synthesis and Molekular Structures of N‐substituted Diethylgallium‐2‐pyridylmethylamides (2‐Pyridylmethyl)(tert‐butyldimethylsilyl)amine ( 1a ) and (2‐pyridylmethyl)‐di(tert‐butyl)silylamine ( 1b ) form with triethylgallane the corresponding red adducts 2a and 2b via an additional nitrogen‐gallium bond. These oily compounds decompose during distillation. Heating under reflux in toluene leads to the elimination of ethane and the formation of the red oils of [(2‐pyridylmethyl)(tert‐butyldimethylsilyl)amido]diethylgallane ( 3a ) and [(2‐pyridylmethyl)‐di(tert‐butyl)silylamido]diethylgallane ( 3b ). In order to investigate the thermal stability solvent‐free 3a is heated up to 400 °C. The elimination of ethane is observed again and the C‐C coupling product N, N′‐Bis(diethylgallyl)‐1, 2‐dipyridyl‐1, 2‐bis(tert‐butyldimethylsilyl)amido]ethan ( 4 ) is found in the residue. Substitution of the silyl substituents by another 2‐pyridylmethyl group and the reaction of this bis(2‐pyridylmethyl)amine with GaEt₃ yield triethylgallane‐diethylgallium‐bis(2‐pyridylmethyl)amide ( 5 ). The metalation product adds immediately another equivalent of triethylgallane regardless of the stoichiometry. The reaction of GaEt₃ with 2‐pyridylmethanol gives quantitatively colorless 2‐pyridylmethanolato diethylgallane ( 6 ).     

NMR.-Investigation of the Formaldehyde Addition and Oligomerisation Equilibria in the System Formaldehyde/Water/Acetic Acid/Hydrochloric Acid

An NMR. investigation of the state of formaldehyde in acidic solutions has been carried out. Solutions of DCl/D₂O/CD₃COOD containing two sources of formaldehyde, i.e. paraformaldehyde (I) and trioxane (II), were used for this purpose. In systems I and II the effect of various D₂O/CD₃COOD ratios, at a constant DCl concentration, was studied, while for II the effect of changing DCl concentration was also investigated. The results show that in aqueous solution, formaldehyde exists primarily as the monomeric and linear oligomeric forms of methylene glycol. Reducing the amount of D₂O (at constant DCl concentration), while increasing the CD₃COOD content, results in an increase in the polymeric species and in trioxane. In addition, substitution of water by acetic acid results in systems that are catalytically more active than aqueous solutions of the same hydrochloric acid concentration. Along with the usual polymer-monomer equilibria which exist in such solutions, side reactions of methylene glycol with the hydrochloric acid present also occur to a small extent, e.g. acetylation, substitution of OH by Cl and the Cannizzaro reaction. It is suggested that these findings will result in a better understanding of the formaldehyde crosslinking reactions in cotton cellulose.