Über das Eulersche Summierungsverfahren

Ohne Zusammenfassung     

Über die partiellen Differentialgleichungen der schwingenden Saiten und Membranen

Ohne Zusammenfassung     

Remarks on semilinear partial functional-differential equations with infinite delay

In this paper we will be concerned with the abstract semilinear equation x(Φ)(t) = Ax(Φ)(t) + F(t, x_t(Φ)), t ? τ, x_τ(Φ) = Φ, where A represents the infinitesimal generator of a linear C₀-semigroup in a Banach space and x_～(Φ) denotes the segment of the solution x due to the initial function Φ taken from ?∞ up to t. Conditions for existence, continuous dependence, and regularity of solutions are given which are independent of the topology of the phase space, as well as conditions which guarantee the compactness of bounded orbits, even if exp(At) is not compact for t > 0.     

Large antipodal families

A family {A _i | i ∈ I} of sets in ℝ ^d is antipodal if for any distinct i, j ∈ I and any p ∈ A _i , q ∈ A _j , there is a linear functional ϕ:ℝ ^d → ℝ such that ϕ(p) ≠ ϕ(q) and ϕ(p) ≤ ϕ(r) ≤ ϕ(q) for all r ∈ ∪ _i∈I A _i . We study the existence of antipodal families of large finite or infinite sets in ℝ³. The research was supported by the Hungarian-South African Intergovernmental Scientific and Technological Cooperation Programme, NKTH Grant no. ZA-21/2006 and South African National Research Foundation Grant no. UID 61853, as well as Hungarian National Foundation for Scientific Research Grants no. NK 67867, no. T47102, and no. K72537.     

Carbon incorporation in Pd(111) by adsorption and dehydrogenation of ethene

The decomposition of ethene on the Pd(111) surface was studied at effective pressures in the 10(-8) to 10(-7) mbar range and at sample temperatures between 300 and 700 K, using an effusive capillary array beam doser for directional adsorption, LEED, AES, temperature programmed reaction, and TDS. In the temperature range of 350-440 K increasingly stronger dehydrogenation of the ethene molecule is observed. Whereas at 350 K an ethylidyne adlayer is still present after adsorption, already at temperatures around 440 K complete coverage of the surface by carbon is attained, while the bulk still retains the properties of pure Pd. Beyond 440 K a steady-state surface C coverage is established, which decreases with temperature and is determined by detailed balancing between the ethene gas-phase adsorption rate and the migration rate of carbon into the Pd bulk. This process gives rise to the formation of a "partially carbon-covered Pd(x)C(y) surface". Above 540 K the surface-bulk diffusion of adsorbed carbon becomes fast, and in the UHV experiment the ethene adsorption rate becomes limited by the ethene gas-phase supply. The carbon bulk migration rate and the steady-state carbon surface coverage were determined as a function of the sample temperature and the ethene flux. An activation energy of 107 kJ mol(-1) for the process of C diffusion from surface adsorption sites into the subsurface region was derived in the temperature range of 400-650 K by modeling the C surface coverage as a function of temperature on the basis of steady-state reaction kinetics, assuming a first-order process for C surface-subsurface diffusion and a second-order process for C(ads) formation by dissociative C2H4 adsorption.     

Protection‐Group‐Free Synthesis of Sequence‐Defined Macromolecules via Precision λ‐Orthogonal Photochemistry

An advanced light‐induced avenue to monodisperse sequence‐defined linear macromolecules via a unique photochemical protocol is presented that does not require any protection‐group chemistry. Starting from a symmetrical core unit, precision macromolecules with molecular weights up to 6257.10 g mol^?1 are obtained via a two‐monomer system: a monomer unit carrying a pyrene functionalized visible light responsive tetrazole and a photo‐caged UV responsive diene, enabling an iterative approach for chain growth; and a monomer unit equipped with a carboxylic acid and a fumarate. Both light‐induced chain growth reactions are carried out in a λ‐orthogonal fashion, exciting the respective photosensitive group selectively and thus avoiding protecting chemistry. Characterization of each sequence‐defined chain (size‐exclusion chromatography (SEC), high‐resolution electrospray ionization mass spectrometry (ESI‐MS), and NMR spectroscopy), confirms the precision nature of the macromolecules.     

Hydrogen bonds and local symmetry in the crystal structure of gibbsite

First‐principles quantum mechanical calculations of NMR chemical shifts and quadrupolar parameters have been carried out to assign the ²⁷Al MAS NMR resonances in gibbsite. The ²⁷Al NMR spectrum shows two signals for octahedral aluminum revealing two aluminum sites coordinated by six hydroxyl groups each, although the crystallographic positions of the two Al sites show little difference. The presence of two distinguished ²⁷Al NMR resonances characterized by rather similar chemical shifts but quadrupolar coupling constants differing by roughly a factor of two is explained by different character of the hydrogen bonds, in which the hydroxyls forming the corresponding octahedron around each aluminum site, are involved. The Al‐I site characterized by a C_Q = 4.6 MHz is surrounded by OH? groups participating in four intralayer and two interlayer hydrogen bonds, while the Al‐II site with the smaller quadrupolar constant (2.2 MHz) is coordinated by hydroxides, of which two point toward the intralayer cavities and four OH‐bonds are aligned toward the interlayer gallery. In high‐resolution solid‐state ¹H CRAMPS (combination of rotation and multiple‐pulse spectroscopy) four signals with an intensity ratio of 1:2:2:1 are resolved which allow to distinguish six nonequivalent hydrogen sites reported in the gibbsite crystal structure and to ascribe them to two types of structural OH groups associated with intralayer and interlayer hydrogen bonds. This study can be applied to characterize the gibbsite‐like layer—intergallery interactions associated with hydrogen bonding in the more complex systems, such as synthetic aluminum layered double hydroxides. Copyright © 2010 John Wiley & Sons, Ltd.     

Origin of the different reactivity of the high-valent coinage-metal complexes [RCuiiiMe3]− and [RAgiiiMe3]− (R=allyl)**

High-valent tetraalkylcuprates(iii ) and -argentates(iii ) are key intermediates of copper- and silver-mediated C−C coupling reactions. Here, we investigate the previously reported contrasting reactivity of [RMⁱⁱⁱ Me₃]⁻ complexes (M=Cu, Ag and R=allyl) with energy-dependent collision-induced dissociation experiments, advanced quantum-chemical calculations and kinetic computations. The gas-phase fragmentation experiments confirmed the preferred formation of the [RCuMe]⁻ anion upon collisional activation of the cuprate(iii ) species, consistent with a homo-coupling reaction, whereas the silver analogue primarily yielded [AgMe₂]⁻, consistent with a cross-coupling reaction. For both complexes, density functional theory calculations identified one mechanism for homo coupling and four different ones for cross coupling. Of these pathways, an unprecedented concerted outer-sphere cross coupling is of particular interest, because it can explain the formation of [AgMe₂]⁻ from the argentate(iii ) species. Remarkably, the different C−C coupling propensities of the two [RMⁱⁱⁱ Me₃]⁻ complexes become only apparent when properly accounting for the multi-configurational character of the wave function for the key transition state of [RAgMe₃]⁻. Backed by the obtained detailed mechanistic insight for the gas-phase reactions, we propose that the previously observed cross-coupling reaction of the silver complex in solution proceeds via the outer-sphere mechanism.     

Radiation-Induced Oxidation Reactions of 2-Selenouracil in Aqueous Solutions: Comparison with Sulfur Analog of Uracil

One-electron oxidation of 2-selenouracil (2-SeU) by hydroxyl (^●OH) and azide (^●N₃) radicals leads to various primary reactive intermediates. Their optical absorption spectra and kinetic characteristics were studied by pulse radiolysis with UV-vis spectrophotometric and conductivity detection and by the density functional theory (DFT) method. The transient absorption spectra recorded in the reactions of ^●OH with 2-SeU are dominated by an absorption band with an λ_max = 440 nm, the intensity of which depends on the concentration of 2-SeU and pH. Based on the combination of conductometric and DFT studies, the transient absorption band observed both at low and high concentrations of 2-SeU was assigned to the dimeric 2c-3e Se-Se-bonded radical in neutral form (2^●). The dimeric radical (2^●) is formed in the reaction of a selenyl-type radical (6^●) with 2-SeU, and both radicals are in equilibrium with K_eq = 1.3 × 10⁴ M⁻¹ at pH 4 (below the pK_a of 2-SeU). Similar equilibrium with K_eq = 4.4 × 10³ M⁻¹ was determined for pH 10 (above the pK_a of 2-SeU), which admittedly involves the same radical (6^●) but with a dimeric 2c-3e Se-Se bonded radical in anionic form (2^●−). In turn, at the lowest concentration of 2-SeU (0.05 mM) and pH 10, the transient absorption spectrum is dominated by an absorption band with an λ_max = 390 nm, which was assigned to the ^●OH adduct to the double bond at C5 carbon atom (3^●) based on DFT calculations. Similar spectral and kinetic features were also observed during the ^●N₃-induced oxidation of 2-SeU. In principle, our results mostly revealed similarities in one-electron oxidation pathways of 2-SeU and 2-thiouracil (2-TU). The major difference concerns the stability of dimeric radicals with a 2c-3e chalcogen-chalcogen bond in favor of 2-SeU.     

Possibility to Biotransform Anthracyclines by Peroxidases Produced by Bjerkandera adusta CCBAS 930 with Reduction of Geno- and Cytotoxicity and Pro-Oxidative Activity

The aim of this study was to evaluate the bioremoval mechanism of anthracycline antibiotics by the white-rot fungus B. adusta CCBAS 930. The activity of oxidoreductases and levels of phenolic compounds and free radicals were determined during the biotransformation of anthraquinone antibiotics: daunomycin (DNR) and doxorubicin (DOX) by B. adusta strain CCBAS 930. Moreover, phytotoxicity (Lepidium sativum L.), ecotoxicity (Vibrio fischeri), genotoxicity and cytotoxicity of anthraquinone dyes were evaluated before and after biological treatment. More than 80% and 90% of DNR and DOX were removed by biodegradation (decolorization). Initial solutions of DNR and DOX were characterized by eco-, phyto-, geno- and cytotoxicity. Despite efficient decolorization, secondary metabolites, toxic to bacteria, formed during biotransformation of anthracycline antibiotics in B. adusta CCBAS 930 cultures. DNR and DOX metabolites did not increase reactive oxygen species (ROS) production in human fibroblasts and resazurin reduction. DNR metabolites did not change caspase-3 activity.