Random iterations, fixed points and invariant CRF-horospheres in complex Banach spaces

For holomorphic noncontractive maps on (not necessarily bounded) domains in complex Banach spaces, we establish the conditions guaranteeing locally uniform convergence of random iterations and study the existence of fixed points and boundary behaviour of iterations. In particular, we show that the problem, concerning the existence of the horospheres determined by Carathéodory-Reiffen-Finsler pseudometrics defined on unbounded domains, has the solution and we prove new results of type of Julia's lemma and Wolff's theorem.     

On the Wigner-Eckart theorem for tensor operators connected with compact matrix quantum groups

In this Letter, the notion of a tensor operator connected with a unitary, smooth, finite-dimensional representation of a compact, matrix quantum group is introduced and investigated. It is proved that, for compact matrix, simply reducible quantum groups, there exists a theorem analogous to the famous Wigner-Eckart theorem.     

Adaptation of an echelle spectrograph to a large CCD detector

A broad range echelle spectrograph with a CCD matrix detector is developed for different applications in atomic spectroscopy. The compact optical design in combination with a dispersive entrance slit illumination offers a low stray light level and high throughput in the UV spectral region comparable only with spectrographs of higher focal length. Ray tracing calculations for typical wavelengths and the multi-line spectrum of an iron arc show the excellent overall spectrum quality. The subtraction of two partial spectra of different steel alloys demonstrates the spectra evaluation possibilities of the CCD spectrograph.     

Bonding in HNO-myoglobin as characterized by X-ray absorption and resonance raman spectroscopies

The EXAFS and resonance Raman spectra on the HNO-myoglobin adduct, 1, are consistent with the presence of HNO bound to a heme center. The three-dimensional structure about the heme center of 1 obtained from multiple-scattering (MS) analysis of the EXAFS of the heme protein yielded an Fe-N-O bond angle of 131 degrees and an Fe-N bond length of 1.82 A, which compare well with published values for model complexes containing RNO ligands. Resonance Raman spectra identified the nu(N=O) stretch at 1385 cm-1 (confirmed by 15N labeling), which corresponds well with those reported for small molecule HNO complexes. The wavelength of the nu(Fe-N) at 636 cm-1 of 1 is significantly higher than those of MbIINO and MbIIINO (554 and 595 cm-1, respectively). The XAFS, XANES, and resonance Raman data are all consistent with the structure deduced from the NMR experiments, providing more detail on the bonding between HNO and the metal center.     

Retention Behavior of Polyethylene Glycol and Its Influence on Protein Elution on Hydrophobic Interaction Chromatography Media

The retention behavior of polyethylene glycol (PEG) on different types of hydrophobic interaction chromatography (HIC) resins containing butyl, octyl, and phenyl ligands was analyzed. An incomplete elution or splitting of the polymer peak into two parts was observed, where the first one was eluted at the dead time of the column, whereas the second one was strongly retained. The phenomenon was attributed to conformation changes of the polymer upon its adsorption on hydrophobic surface. The effect enhanced with increasing molecular weight of the polymer and hydrophobicity of the HIC media. Addition of PEG to the mobile phase reduced binding of proteins to HIC resins, which was demonstrated with two model systems: lysozyme (LYZ) and immunoglobulin G (IgG), and their mixtures. In case of LYZ, the presence of PEG caused reduction in the protein retention, whereas for IgG—a decrease in efficiency of the protein capture. The effect depended on the adsorption pattern of PEG; it was pronounced in the systems in which conformational changes of the polymer were suggested to occur.     

Effect of para-substituents on alkaline earth metal ion extraction by proton di-ionizable calix[4]arene-crown-6 ligands in cone, partial-cone and 1,3-alternate conformations

Two carboxylic acid or N-(X)sulfonyl carboxamide groups were incorporated into calix[4]arene-crown-6 compounds to afford di-ionizable ligands for use in divalent metal ion separations. Acidities of the N-(X)sulfonyl carboxamide groups were tuned by variation of the electron-withdrawing properties of X. Cone, partial-cone and 1,3-alternate conformations were obtained by different synthetic strategies and their structures verified by NMR spectroscopy. Competitive solvent extractions of alkaline earth metal cations from aqueous solutions into chloroform were performed and the results compared with those reported previously for di-ionizable p-tert-butylcalix[4]arene-crown-6 analogues to probe the influence of the para-substituent on the calix[4]arene scaffold on extraction selectivity and efficiency.     

Bestimmung der Geschwindigkeitskonstante der Bromierungsreaktion von Acetanilid mittels Titrationsmethode in diffuser Schicht an der rotierenden Ring-Scheiben-Elektrode

The kinetics of the bromination of acetanilide has been studied with the diffusion layer titration method. The results have been obtained using the apparatus which consists of the ring-disc electrode and an amperostat-potentiostat system. Dependence of the ring current on the disc current has been determined as a function of rotation speeds of the electrode, of the solution concentration and temperature. It has been shown the bromination reaction of acetanilide exhibits by first order kinetics. In that case Br₂ and Br₃ ^? are the brominating species. The rate of bromination changes with the concentration of the Br^? ions. This reaction rate depends on reactions of molecular bromine with acetanilide. For 0.033<[Br^?]<0.173M the rate constant changes in the following range: $$17530M^{ - 1} s^{ - 1}< k< 6400M^{ - 1} s^{ - 1} ([H + ] = 1,34;T = 298K)$$      

Functions generating (m,M, $$varvec{Psi }$$ )-Schur-convex sums

Aequationes mathematicae - The notion of $$(m,M,Psi )$$ -Schur-convexity is introduced and functions generating $$(m,M,Psi )$$ -Schur-convex sums are investigated. An extension of the...