Shift operators contained in contractions, pseudocontinuable Schur functions and orthogonal systems on the unit circle

The main aim of this paper is to establish the connection between well-known criteria for the pseudocontinuability of a non-inner Schur function ?? in the unit disk (see Theorems 3.9, 4.2). In a canonical way we associate a probability measure ?? on the unit circle with ??. One of the two criteria will be reformulated in the face of ??, whereas the other one is drafted in view of a completely nonunitary contraction T having ?? as corresponding characteristic function. Our main result clarifies an immediate connection between the above-mentioned two criteria. In this way, we rewrite these criteria in terms of orthogonal systems with respect to the measure ?? (see Theorem 7.2).     

SO-I: a surrogate model algorithm for expensive nonlinear integer programming problems including global optimization applications

This paper presents the surrogate model based algorithm SO-I for solving purely integer optimization problems that have computationally expensive black-box objective functions and that may have computationally expensive constraints. The algorithm was developed for solving global optimization problems, meaning that the relaxed optimization problems have many local optima. However, the method is also shown to perform well on many local optimization problems, and problems with linear objective functions. The performance of SO-I, a genetic algorithm, Nonsmooth Optimization by Mesh Adaptive Direct Search (NOMAD), SO-MI (Müller et al. in Comput Oper Res 40(5):1383–1400, 2013), variable neighborhood search, and a version of SO-I that only uses a local search has been compared on 17 test problems from the literature, and on eight realizations of two application problems. One application problem relates to hydropower generation, and the other one to throughput maximization. The numerical results show that SO-I finds good solutions most efficiently. Moreover, as opposed to SO-MI, SO-I is able to find feasible points by employing a first optimization phase that aims at minimizing a constraint violation function. A feasible user-supplied point is not necessary.     

Aetherische Oele

Ohne Zusammenfassung     

Spin-state dynamics of a photochromic iron(II) complex and its immobilization on oxide surfaces via phenol anchors

This work presents a detailed study of the photo-induced spin-state dynamics of the photochromic iron(II) complex 1, where the metal ion is in the field of a tripodal hexa-imine ligand with protolysable phenol groups. The nature of the complex’s ground state has been identified as a spin singlet by ¹H NMR and steady-state UV/vis spectroscopies, and its distorted octahedral structure was analyzed via crystal structure determination. Sub-picosecond and nanosecond time-resolved laser flash photolysis experiments identify the long-lived quintet state of 1 as the selective product of photoexcitation in the UV/vis spectral region. Thermal barriers of spin-state interconversion as a function of solvent and added base are derived from temperature-dependent rates of transient decay. Ground-state recovery is found to be significantly affected by the solvent and is strongly enhanced, in particular, by base-driven solvolysis of the ligand’s phenol groups. Partial spontaneous deprotonation of the phenolic hydroxyl groups of 1 seems to prevail on metal oxide surfaces, i.e. on alumina. Composite materials, like 1 at Al₂O₃, that retain the characteristic spectral features of the parent iron(II) complex can be readily obtained by wet impregnation of hydrous alumina with solutions of 1.     

Quasi-homogeneous hydrogenation with platinum and palladium nanoparticles stabilized by dendritic core-multishell architectures

Platinum and palladium nanoparticles, supported and stabilized by polymeric core-shell architectures, proved to be active catalysts for hydrogenation reactions. Here, two different reactions were used as probes to investigate the influence of the polymeric support: the hydrogenation of α-methyl styrene (AMS) to cumene and the partial hydrogenation of 1,5-cyclooctadiene (COD). We found that the stability of the nanoparticles and the rate of reaction are higher in the presence of a hydrophobic octadecyl shell within a three-shell polymer system. The kinetic study of AMS hydrogenation showed much higher activities for palladium nanoparticles than for platinum nanoparticles, and the obtained results (e.g., 35 kJ/mol for the activation energy) are of the same order of magnitude as reported earlier for palladium supported on alumina. A methanol/n-heptane biphasic mixture was tested for catalyst recycling and allowed for highly efficient catalyst separation with very low metal leaching.     

On the sequences of the Weyl semi-radii associated with matricial Carathéodory and Schur sequences in both nondegenerate and degenerate cases

In this paper we discuss Weyl matrix balls in the context of the matricial versions of the classical interpolation problems named after Carathéodory and Schur. Our particular focus will be on studying the monotonicity of suitably normalized semi-radii of the corresponding Weyl matrix balls. We, furthermore, devote a fair bit of attention to characterizing the case in which equality holds for particular matricial inequalities. Solving these problems will provide us with a new perspective on the role of the central functions for the classes of Carathéodory and Schur.     

Tuning the hydrophobicity of mica surfaces by hyperthermal Ar ion irradiation

The hydrophobicity of surfaces has a strong influence on their interactions with biomolecules such as proteins. Therefore, for in vitro studies of bio-surface interactions model surfaces with tailored hydrophobicity are of utmost importance. Here, we present a method for tuning the hydrophobicity of atomically flat mica surfaces by hyperthermal Ar ion irradiation. Due to the sub-100 eV energies, only negligible roughening of the surface is observed at low ion fluences and also the chemical composition of the mica crystal remains almost undisturbed. However, the ion irradiation induces the preferential removal of the outermost layer of K(+) ions from the surface, leading to the exposure of the underlying aluminosilicate sheets which feature a large number of centers for C adsorption. The irradiated surface thus exhibits an enhanced chemical reactivity toward hydrocarbons, resulting in the adsorption of a thin hydrocarbon film from the environment. Aging these surfaces under ambient conditions leads to a continuous increase of their contact angle until a fully hydrophobic surface with a contact angle >80° is obtained after a period of about 3 months. This method thus enables the fabrication of ultrasmooth biological model surfaces with precisely tailored hydrophobicity.     

Ultrafast dynamics of isolated fluorenone

The ultrafast dynamics of isolated 9-fluorenone was studied by femtosecond time-resolved photoionization and photoelectron spectroscopy. The molecule was excited around 264-266 nm into the S(6) state. The experimental results indicate that the excitation is followed by a multistep deactivation. A time constant of 50 fs or less corresponds to a fast redistribution of energy within the initially excited manifold of states, i.e., a motion away from the Franck-Condon region. Internal conversion to the S(1) state then proceeds within 0.4 ps. The S(1) state is long-lived, and only a lower bound of 20 ps can be derived. In addition, we computed excited state energies and oscillator strengths by TD-DFT theory, supporting the interpretation of the experimental data.