Equivalences between categories of modules and categories of comodules

We show the close connection between apparently different Galois theories for comodules introduced recently in [J. Gomez-Torrecillas and J. Vercruysse, Comatrix corings and Galois Comodules over firm rings, Algebr. Represent. Theory, 10 （2007）, 271 306] and [Wisbauer, On Galois comodules, Comm. Algebra 34 （2006）, 2683-2711]. Furthermore we study equivalences between categories of comodules over a coring and modules over a firm ring. We show that these equivalences are related to Galois theory for comodules.     

Molecular complexity from aromatics: synthesis of highly functionalized spiro δ-lactones

A novel, general, and efficient method has been developed for the synthesis of highly functionalized spiro δ-lactones from aromatic precursors. Our methodology involves a tandem oxidative dearomatization-rearrangement of tertiary furyl carbinols and ring-closing metathesis as key features. This method allows an access to the spirolactones attached to carbocycles of various sizes.     

Thermal behavior of aromatic polyamic acids and polyimides containing oxadiazole rings

Two aromatic polyimides and the corresponding poly(amic acid)s, with oxadiazole and para/meta phenoxyphenylene rings in the backbone, were synthesized and the structure — thermal properties correlation was followed by dynamic mechanical analysis. Concerning the poly(amic acid)s, the glass transition domain was emphasized only for the compound with meta-oriented rings because the process of imidization takes place with increasing temperature. A multiplex experiment was performed to calculate the activation energy of the transition localized under 200°C. Consecutive heating-cooling-heating cycles were accomplished. All phenomena are discussed by cross-examination of the storage modulus (E′), loss modulus (E″) and loss factor tanδ variation with temperature.     

亚直不可约环成为全矩阵环的条件

给出了亚直不可约环是除环上的全矩阵环的一个新的条件。     

Quadratic characters in groups of odd order

We prove that in a finite group of odd order, the number of irreducible quadratic characters is the number of quadratic conjugacy classes.     

Impurity effects in the optical absorption of quantum rings

We study the interplay between impurity scattering and Coulomb interaction effects in the absorption spectrum of neutral bound magnetoexcitons confined in quantum-ring structures. Impurity scattering breaks the rotational symmetry of the ring system, introducing characteristic features in the optical emission. Signatures of the optical Aharonov–Bohm effect are still present for weak scattering and strong Coulomb screening. Furthermore, an impurity-induced modulation of the absorption strength is present even for a strong impurity potential and low screening. This behavior is likely responsible of recent experimental observations in quantum-ring structures.     

Application of X-ray diffraction, micromagnetic and hole drilling methods for residual stress determination in a ball bearing steel ring

A basic understanding of distortion problems requires the analysis of a complete manufacturing process including an almost complete overview of residual stress states in the component during each production step. To reduce the measurement time in the future, three measurements methods (X-ray diffraction, micromagnetic and blind hole drilling methods) have been used to analyze residual stress states in machined AISI 52100 ball bearing rings. X-ray diffraction was used as a state-of-the-art method for machining induced residual stresses with pronounced gradients. The ring exhibited a complex residual stress state with high tensile residual stresses at the surface, a strong gradient in depth, and also showed some variation along the outer circumference due to a superimposition of machining induced residual stresses and effects from the clamping device process. Due to this surface state, micromagnetic signals depend on the analyzing frequency. A calibration of the signals was only possible with the X-ray diffraction data. The results of the three different measurement methods correlate reasonably well.     

Five-membered ring chelate complexes of Ni(II), Pd(II) and Pt(II) derived of di-(2-pyridyl)-N-ethylimine

Cis-diaquobis{di-(2-pyridyl)-N-ethylimine}nickel(II) chloride (2) was obtained from the reaction of di-(2-pyridyl)-N-ethylimine (1) and [NiCl₂dppe] [dppe = cis-1,2-bis(diphenylphosphino)ethylene] in a 2:1 ratio in hot acetonitrile. Cis-dichloro{di-(2-pyridyl)-N-ethylimine}palladium(II) (3) and cis-dichloro{di-(2-pyridyl)-N-ethylimine}platinum(II) (4) complexes were obtained from the reaction of MCl₂ (M = Pd, Pt) and (1) in equimolar ratio in hot acetonitrile. Compounds 1–4 were characterized by IR spectroscopy, elemental analysis, and mass spectrometry; the complexes 3 and 4 were characterized in solution by NMR. In addition, solid state structures of compounds 1–4 were determined using single crystal X-ray diffraction analyses. X-ray diffraction data of the complexes 3 and 4 showed a distorted square planar local geometry at palladium and platinum atoms with the chlorine atoms in a cis-coordination; in 2 a local octahedral geometry at nickel atom was observed. Complexes 3 and 4 are arranged as dimers with a M?M distance of 3.4567(4) Å (M = Pd) and 3.4221(4) Å (M = Pt), respectively; 2 consists of units linked by intermolecular hydrogen bonding.     

关于内射模的P-平坦性

通过引用P-平坦模的定义,引入了右IPF环的概念,推广了右IF环的概念,这对研究IF环及QF环具有重要的作用,同时对右IPF环的性质作了一些刻画,得到了右IPF环的若干个等价命题;最后,用P-平坦模及右IPF环推出了正则环的一些等价条件．