Perturbation theory of selfadjoint matrices and sign characteristics under generic structured rank one perturbations

For selfadjoint matrices in an indefinite inner product, possible canonical forms are identified that arise when the matrix is subjected to a selfadjoint generic rank one perturbation. Genericity is understood in the sense of algebraic geometry. Special attention is paid to the perturbation behavior of the sign characteristic. Typically, under such a perturbation, for every given eigenvalue, the largest Jordan block of the eigenvalue is destroyed and (in case the eigenvalue is real) all other Jordan blocks keep their sign characteristic. The new eigenvalues, i.e. those eigenvalues of the perturbed matrix that are not eigenvalues of the original matrix, are typically simple, and in some cases information is provided about their sign characteristic (if the new eigenvalue is real). The main results are proved by using the well known canonical forms of selfadjoint matrices in an indefinite inner product, a version of the Brunovsky canonical form and on general results concerning rank one perturbations obtained.     

3‐Oxa‐6,8‐diaza‐1,2:4,5‐dibenzocycloocta‐1,4‐dien‐7‐one: a three‐dimensional network assembled by hydrogen‐bonding, π–π and edge‐to‐face interactions

The title compound, C₁₃H₁₀N₂O₂, is the first structure in which the urea moiety is incorporated into an eight‐membered ring. Two mol­ecules are found in the asymmetric unit, which are almost identical in their conformation and their hydrogen‐bond pattern. The carbonyl O atom acts as a double acceptor for the NH groups of two adjacent mol­ecules. In this way, infinite tapes are formed, which are connected viaπ–π and edge‐to‐face interactions in the second and third dimension. This hierarchical order of interactions is confirmed by molecular mechanics calculations. Force‐field and semi‐empirical calculations for a single mol­ecule did not find the envelope conformation present in the crystal, indicating instead a C_s conformation. Only with a model consisting of a hydrogen‐bonded dimer or a larger hydrogen‐bonded section was a conformation found that was similar to the one present in the crystal.     

Preparation and characterization of mesoporous N-doped and sulfuric acid treated anatase TiO2 catalysts and their photocatalytic activity under UV and Vis illumination

Nitrogen-doped TiO₂ catalysts were prepared by a precipitation method. The samples were calcined at 400 °C for 4 h in air. X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), low temperature N₂-adsorption was used for structural characterization and UV-diffuse reflectance (UV-DR) was applied to investigate the optical properties of the as-prepared samples. It was found that microporous N-doped catalysts have solely anatase crystalline structure. Acidic treatment of the calcined samples was performed using sulfuric acid agitation. The crystalline structure remained unchanged due to surface treatment, while the porosity and the surface areas were decreased dramatically. Optical characterization of the doped catalysts showed that they could be excited by visible light photons in the 400–500 nm wavelength range (λ_g,1=390 nm, λ_g,2=510 nm). It was also established that surface treatment enhances the Vis-light absorption of the N-TiO₂ powders. Finally the catalysts were tested in the photocatalytic degradation of phenol in aqueous suspensions. Two different light sources were used; one of them was a UV-rich high pressure Hg-lamp, while the other was a tubular visible light source. We found that using visible light illumination N-doped, acid treated TiO₂ samples were more catalytically active than non-doped TiO₂ catalysts.     

A note on Potter’s theorem for quasi-commutative matrices

We discuss the converse of a theorem of Potter stating that if the matrix equation AB=ωBA is satisfied with ω a primitive qth root of unity, then A^q+B^q=(A+B)^q. We show that both conditions have to be modified to get a converse statement and we present a characterization when the converse holds for these modified conditions and q=3 and a conjecture for the general case. We also present some further partial results and conjectures.     

Eine alternative Synthese des Oligoalumosiloxans [Ph2SiO]8[Al(O)OH]4 und seiner Alkohol‐Addukte

The oligoalumosiloxanes {[Ph₂SiO]₈[Al(O)OH]₄·2,5Et₂O·HOtBu} ( 6 ) and {[Ph₂SiO]₈[Al(O)OH]₄·2Et₂O·2HOiPr} ( 7 ) have been obtained from the reaction of diphenylsilanediol with aluminium‐tri‐tert‐butoxide and aluminium‐tri‐iso‐propoxide in ethyl ether with reasonable yields. In a 1:1 molar mixture of toluene and the respective alcohol (iso‐propanol or tert‐butanol), the ethyl ether molecules in {[Ph₂SiO]₈[Al(O)OH]₄·4Et₂O}, in 6 or 7 can be completely displaced forming the compounds [Ph₂SiO]₈[Al(O)OH]₄·4HOiPr ( 8 ) and [Ph₂SiO]₈[Al(O)OH]₄·nHOtBu ( 9 ). Whereas 6 , 7 and 8 are crystalline, 9 is obtained as a viscous liquid. An X‐ray structure determination on {[Ph₂SiO]₈[Al(O)OH]₄·3Et₂O·HOtBu} reveals different bonding modes of the diethyl ether molecules to the oligoalumosiloxane compared to the tert‐butanol, which forms two hydrogen bonds (one to the OH‐group of the inner Al₄(OH)₄ cycle and one through the alcohol OH‐group to a Si–O–Al moiety. The alcohol adducts have been characterized in solution through ¹H‐, ¹³C‐ and ²⁹Si‐NMR and show dynamic equilibria between the oligoalumosiloxane [Ph₂SiO]₈[Al(O)OH]₄ and the alcohol molecules.     

Synthesen und Strukturen der Lithiumtitanate(III) und ‐(IV), (py)2Li[(py)2Ti(OPh)4] und (py)2Li[(py)Ti(OPh)5]

Syntheses and Structures of the Lithiumtitanates(III)/(IV) (py)₂Li[(py)₂Ti(OPh)₄] and (py)₂Li[(py)Ti(OPh)₅] The new lithiumtitanates (py)₂Li[(py)₂Ti(OPh)₄] ( 1 ) and (py)₂Li[(py)Ti(OPh)₅] ( 2 ) have been obtained from the reaction of titaniumtrichloride (respectively titaniumtetrachloride 2 ) with LiOPh in the presence of the base pyridine (py). The crystal structures of both compounds show that the titanium atoms are in the centres of distorted octahedral coordination figures. In compound 1 , four oxygen and two nitrogen atoms (in cis orientation) are bonded to titanium, whereas in 2 , five oxygen and one nitrogen atom form the coordination polyeder around titanium. In both compounds, the lithium atoms are attached through phenolate bridges to the octahedra. The titanate (py)₂Li[(py)₂Ti(OPh)₄] ( 1 ) has a single absorption band in the visible region of the UV‐spectrum showing a shoulder shifted to the bathochromic region, due to the Jahn‐Teller‐effect for d¹‐systems.     

Hybrid ZnO/polymer thin films prepared by RF magnetron sputtering

Zinc oxide/poly(acrylic acid) (ZnO/PAA) multilayered hybrid films with different layer thicknesses were prepared by radio frequency magnetron sputtering. Zinc peroxide was used as precursor materials for the preparation of ZnO layers, since the zinc peroxide decomposes to ZnO during the film deposition. The films have a high transmittance in the visible region and exhibit visible photoluminescence emission. The band gap energy of the films—determined by the Tauc relationship—decreases with increasing layer thickness (3.40–3.36 eV) due to the increasing crystalline size of the ZnO particles. The morphological investigations showed that a real layered hybrid film structure formed.     

Synchrotron Radiation and Neutrons in Art and Archaeology (SR2A) Conference 2016

The seventh edition of the international conference on Synchrotron Radiation and Neutrons in Art and Archaeology (SR2A 2016) was held September 6–8, 2016, at the Stock Exchange Room of The Art Institute of Chicago, USA. The conference was jointly organized by seven research laboratories and museums; more precisely, the Center for Scientific Studies in the Arts (NU-ACCESS) of Northwestern University, the Art Institute of Chicago, the Field Museum Chicago, the Advanced Photon Source (APS), the Oriental Institute Chicago, the Detroit Institute of Arts, and the Indianapolis Museum of Art, in close interaction with the SR2A International Committee. Nine years after the organization of the first SR2A conference in Grenoble, the Art Institute hosted the second biennial interdisciplinary meeting in the US.