Identity principles for commuting holomorphic self-maps of the unit disc

Let f,g be two commuting holomorphic self-maps of the unit disc. If f and g agree at the common Wolff point up to a certain order of derivatives (no more than 3 if the Wolff point is on the unit circle), then f≡g.     

Working Methods Paper: Critical considerations with respect to the identification of tin species in the environment

Biogeochemical pathways of tin species in the environment are still controversial, e.g. with regard to methylation and transmethylation phenomena, owing to the fact that the identification of methylated tin-compounds is often difficult. The previous tentative identification of a mixed methylbutyltin compound in sediment and biological samples by GC/AAS after hydride generation gave an illustration of this problem. This compound was previously identified in sediments by other authors and also suspected to occur in a contaminated sediment sample from the Boyardville Marina, France. The retention time obtained by GC/AAS corresponded to the actual retention time of a mixed methylbutyltin calibrant. However, additional checks demonstrated that the compound detected was actually monophenyltin. This evidence was produced by a thorough analysis of a selected sediment sample by alternative techniques such as GC/AAS and GC/AES after pentylation, GC/FPD and GC/MS. The results presented highlight the need for a full identification of compounds to avoid mis-interpretation.     

Ritt’s theorem and the Heins map in hyperbolic complex manifolds

Let X be a Kobayashi hyperbolic complex manifold, and assume that X does not contain compact complex submanifolds of positive dimension (e.g., X Stein). We shall prove the following generalization of Ritt’s theorem: every holomorphic self-map f:X→X such that f(X) is relatively compact in X has a unique fixed point τ(f) ∈ X, which is attracting. Furthermore, we shall prove that τ(f) depends holomorphically on f in a suitable sense, generalizing results by Heins, Joseph-Kwack and the second author.     

Terpyridine Zn(II), Ru(III), and Ir(III) complexes: the relevant role of the nature of the metal ion and of the ancillary ligands on the second-order nonlinear response of terpyridines carrying electron donor or electron acceptor groups

Coordination of 4'-(C6H4-p-X)-2,2':6',2'-terpyridines [X = NO2, NBu2, (E)-CH=CH-C6H4-p-NBu2, (E,E)-(CH=CH)2-C6H4-p-NMe2] to Zn(II), Ru(III), and Ir(III) metal centers induces a significant enhancement of the absolute value of the second-order nonlinear optical (NLO) response of the terpyridine, measured by means of both electric field induced second harmonic generation and solvatochromic methods. By varying the nature of the metal center, the enhanced second-order NLO response shifts from positive to negative. Such a shift is controlled by electronic charge-transfer transitions, such as metal-to-ligand or ligand-to-metal transitions, in addition to the intraligand charge transfer. The enhancement generated by coordination is also controlled by the chelation effect and by fine-tuning of the ancillary ligands.     

Thermal decomposition products of copoly(arylene ether sulfone)s characterized by direct pyrolysis mass spectrometry

Pyrolysis products with mass of up to 850 Da were detected by direct pyrolysis mass spectrometric (DPMS) analysis of a series of copoly(arylene ether sulfone)s (PES-PPO) synthesized by nucleophilic condensation of either 4,4′-dichlorodiphenylsulfone (CDPS) or 4,4′-bis-(4-chlorophenyl sulfonyl) biphenyl (long chain dichloride, LCDC) with different molar ratios of hydroquinone (HQ) or dihydroxydiphenylsulfone (HDPS). Pyrolysis products retaining the repeating units of the initial copolymers were formed at temperatures ranging from 420 °C to 470 °C (near the initial decomposition temperature). At temperatures higher than 450 °C were observed products containing biphenyl units, formed by the elimination process of SO₂ from diphenyl sulfone bridges. Products having biphenyl and dibenzofuran moieties were detected in the mass spectra recorded at temperatures above 550 °C. These units were formed by loss of hydrogen atom from diphenyl ether bridges. Although the EI (18 eV) mass spectra of the pyrolysis products of the samples investigated were very similar, it was found that the relative intensity of some ions reflects the molar composition of the copolymers analysed. Cyclic and linear oligomers with very low molecular mass, present in the crude copolymers, were also detected by DPMS. Thermogravimetric analysis also showed their excellent thermal stability below 400 °C. It indicates that the copolymers yield a char residue of 40-45% at 800 °C, which increases with the PPO mole fraction in the samples.     

Long-wavelength fluorescent indicators for the determination of oxygen partial pressures

A series of stable heterocyclic indicators with λ_ex = 469–566 nm and λ_em = 511–652 nm allows the fluorimetric determination of ca. 1–100% partial pressures of oxygen by quenching of fluorescnce, especially in toluene solution.     

Extraction techniques in speciation analysis of environmental samples

One of the main problems in speciation analysis is that the different species of metals are present in complex matrices at very low concentration levels. Thus it is almost always necessary to separate the analytes of concern from the matrix and to concentrate them up to detectable concentration levels. Special care should be paid during extraction in order to avoid any contamination of samples, losses and changes in speciation of analytes of concern. The most common extraction techniques for speciation analysis of Pb, Sn, Hg, Cr, As, Se and Sb in liquid and solid samples are presented and briefly discussed. Due to the large quantity of material to be covered, speciation of alkyl, aryl, and macromolecular compounds (porphyrines, thioneines, etc.) has not been taken into account.     

Gas chromatographic--mass spectrometric determination of phenylacetic acid in human blood

Phenyl acetic acid, a metabolite of 2-phenyl ethylamine, acts as a neuromodulator in the nigrostriatal dopaminergic pathway stimulating the release of dopamine. The evaluation of phenyl acetic acid concentration in the biological fluid reflects phenyl ethylamine levels thus allowing the assessment of the modulatory role of this endogenous substance. Changes in biological fluids levels of 2-phenylethylamine and/or in its metabolite have been reported in affective disorders, such as depression and schizophrenia. Recently, the occurrence of the "attention deficit hyperactivity syndrome" has been frequently reported in childhood population and involvement of dopaminergic dysfunction in this disease has been suspected. A fast, reliable and reproducible method for the determination of phenyl acetic acid in human blood, is therefore needed in order to have a screening tool for monitoring both healthy childhood population and suspected "attention deficit hyperactivity syndrome" patients. The gas chromatographic-mass spectrometric method here described makes use of a deuterated internal standard in order to overcome problems related to the lack of reproducibility often encountered when a derivatization step is performed.