Über einige neue Pikrate

Ohne Zusammenfassung     

Level of nodes in increasing trees revisited

Simply generated families of trees are described by the equation T(z) = ϕ(T(z)) for their generating function. If a tree has n nodes, we say that it is increasing if each node has a label ∈ { 1,…,n}, no label occurs twice, and whenever we proceed from the root to a leaf, the labels are increasing. This leads to the concept of simple families of increasing trees. Three such families are especially important: recursive trees, heap ordered trees, and binary increasing trees. They belong to the subclass of very simple families of increasing trees, which can be characterized in 3 different ways. This paper contains results about these families as well as about polynomial families (the function ϕ(u) is just a polynomial). The random variable of interest is the level of the node (labelled) j, in random trees of size n ≥ j. For very simple families, this is independent of n, and the limiting distribution is Gaussian. For polynomial families, we can prove this as well for j,n → ∞ such that n − j is fixed. Additional results are also given. These results follow from the study of certain trivariate generating functions and Hwang's quasi power theorem. They unify and extend earlier results by Devroye, Mahmoud, and others. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007     

An analytic approach for the analysis of rotations in fringe-balanced binary search trees

This paper presents an analytic approach to the construction cost of fringe-balanced binary search trees. In [7], Mahmoud used a bottom-up approach and an urn model of Pólya. The present method is top-down and uses differential equations and Hwang's quasi-power theorem to derive the asymptotic normality of the number of rotations needed to construct such afringe balanced search tree. We also obtain the exact expectation and variance with this method. Although Pólya's urn model is no longer needed, we also present an elegant analysis of it based on an operator calculus as in [4].This research was supported by the Austrian Research Society (FWF) under the project number P12599-MAT.     

Perhalogenmethylmercapto-heterocyclen, (VII) [1] konkurrenzreaktionen elektronenarmer,substituierter aromaten um die halogenmethylmercapto- BZW. Chlorgruppe von Cl3-nFnCSCl in starken saeuren

Electron-deficient aromatics, such as 2,5-bis(trifluoromethylmercapto)thiophene ($\text{1a}$) or (trifluoromethylmercapto)benzene ($\text{8a}$), react with F₃CSCl in the presence of F₃CSO₃ as a catalyst to give mainly 3-chloro-2,5-bis(trifluoromethylmercapto)thiophen ($\text{3a}$) and 1-chloro-4- or 2-(trifluoromethylmercapto)benzene ($\text{10}$, respectively. This reaction competes with the one expected to result in 2,3,5-tris(trifluoromethylmercapto)thiophene ($\text{2a}$) and 1,4- and 1,2-bis(trifluoromethylmercapto)benzene ($\text{9}$,$\text{9′}$), respectively. Further reactions of deactivated aromatics with Cl_3-nF_nCSCl show that the chlorine substitution is in general catalysed by strong acids. Reaction mechanisms are proposed for both Substitutions. The Cl_3-nF_nCS group in aromatics exerts a -M-effect in the case of an attack of a positive ion, e.g. H^⊕, the well-known +M-effect in the case of reactions with positively polarized molecules, e.g. CF₃S^β+Cl^β-.     

Formation of Zn(1-x)MnxS nanowires within mesoporous silica of different pore sizes

Arrays of highly ordered Zn(1-x)MnxS quantum wires with x ranging from 0.01 to 0.3 and with lateral dimensions of 3, 6, and 9 nm were synthesized within mesoporous SiO2 host structures of the MCM-41 and SBA-15 type. The hexagonal symmetry of these arrays (space group p6m) and the high degree of order was confirmed by X-ray diffraction and transmission electron microscopy (TEM) studies. Physisorption measurements show the progressive filling of the pores of the SiO2 host structures, while TEM and Raman studies reveal the wire-like character of the incorporated Zn(1-x)MnxS nanostructures. X-ray absorption near-edge structure, extended X-ray absorption fine structure, photoluminescence excitation (PLE), and electron paramagnetic resonance studies confirm the good crystalline quality of the incorporated Zn(1-x)MnxS guest species and, in particular, that the Mn2+ ions are randomly distributed and are situated on tetrahedrally coordinated cation sites of the Zn(1-x)MnxS wires for all x up to 0.3. The amount of Mn2+ ions loosely bound to the surface of the Zn(1-x)MnxS nanowires is less than 4% of the total Mn content even for the 3 nm nanostructures up to the highest Mn content of x = 0.3. The effects of the reduction of the lateral dimensions on electronic properties of the diluted magnetic semiconductor were studied by PLE spectroscopy. Due to the quantum confinement of the excitons in the wires an increase of the direct band gap with decreasing particle size is observed.     

A chemo- and stereoselective reduction of cycloalkynes to (E)-cycloalkenes

A stereoselective entry into (E)-cycloalkenes is described, comprising the ring closing alkyne metathesis (RCAM) of suitable diynes, a ruthenium-catalyzed trans-selective hydrosilylation of the cycloalkynes thus formed, followed by a desilylation of the resulting vinylsilanes mediated by AgF.     

In situ determination of adsorption kinetics of proteins in a finite bath

A method for fast in situ measurement of adsorption kinetics based on a finite bath was developed. We modified the conventional finite bath by replacing the external loop by a dip probe which enables in situ measurement of the concentration change in the contactor. Deposition of adsorbent particles on the reflection surface of the dip probe compromised measurements. Different membranes, a polyamide, a polypropylene and a nylon membrane were tested to protect the internal reflection surface of the dip probe from fouling with adsorbent particles. The nylon membrane provided efficient protection and high mass transfer evaluated by response time experiments. Unspecific adsorption of the model protein on the membrane could also be excluded. To corroborate the measurements of the dip probe the results were compared to a conventional finite bath and to a shallow-bed. The uptake curves for human polyclonal IgG at different concentrationes (0.1-3 g/l) on rProtein A Sepharose FF and MabSelect were used as model system. The effective diffusion coefficients were determined using a pore diffusion model. These values were in good agreement for all methods.