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.     

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.     

Shape recognition of alkylammonium ions by 1,3-bridged calix[5]arene crown-6 ethers: endo- vs exo-cavity complexation

A series of tri-O-substituted 1,3-bridged calix[5]arene crown-6 ethers bearing alkyl, arylalkyl, alkoxyalkyl, and alkoxycarbonylmethyl residues at the lower rim and either (t)()Bu or H substituents at the upper rim have been synthesized. (1)H NMR studies have shown that p-tert-butylcalix[5]crowns, irrespective of the size and nature of their lower rim pendant groups, adopt preorganized conelike conformations, whereas p-H-calix[5]crowns with bulky substituents preferentially exist in solution as partial cone conformers (C(1) symmetry). Calix[5]crown derivatives behave as mono- or ditopic receptors for isomeric butylammonium ions, forming endo-cavity (inside the calixarene cup) and/or exo-cavity (at the crown ether moiety) 1:1 complexes according to the shape of the guest. These two binding modes can be clearly distinguished and monitored by (1)H NMR titration experiments.     

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.     

Determination of picotamide in human plasma and urine by high-performance liquid chromatography.

A high-performance liquid chromatographic method for the determination of picotamide in human plasma and urine is described. After addition of an internal standard (bamifylline), the plasma and urine samples were subjected to liquid-liquid extraction and clean-up procedures. The final extracts were evaporated to dryness and the resulting residues were reconstituted in 100 microliters of methanol-water (50:50, v/v) and chromatographed on a LiChrosorb RP-SELECT B reversed-phase column coupled to an ultraviolet detector monitored at 230 nm. Chromatographic analysis takes about 10 min per sample. The assay was linear over a wide range and has a limit of detection of 0.005 and 0.1 micrograms/ml in plasma and urine, respectively. It was selective for picotamide, accurate and robust and thus suitable for routine assays after therapeutic doses of picotamide.