Maße für gerichtete Geraden und nicht-symmetrische Pseudometriken in der Ebene II

We continue our investigations started in a paper with the same title. The -length of a curve defined in this paper can be written as an integral along the curve. Furthermore, we determine necessary and sufficient conditions for the existence of a measure of orientated lines which generates a given non-symmetric pseudo-metric.

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Herrn Prof. Dr. H.-J. Kanold zum 65. Geburtstag gewidmet     

Zur Charakterisierung einer Klasse von Hyperbelstrukturen

A characterisation of those (B^*G)-Geometries (in the sense of Benz) is given, which can be constructed with the help of nearfields F, char F 2, in which the multiplicative group F^*(·) has a subgroup A with index [F^*:A]=2.

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Werner Burau zum 70. Geburtstag gewidmet     

A central limit theorem for age- and density-dependent population processes

Consider a population consisting of one type of individual living in a fixed region with area A. In [8], we constructed a stochastic population model in which the death rate is affected by the age of the individual and the birth rate is affected by the population density P_A(t), i.e., the population size divided by the area A of the given region. In [8], we proposed a continuous deterministic model which in general is a nonlinear Volterra type integral equation and proved that under appropriate conditions the sequence P_A(t) would converge to the solution P(t) of our integral equation in the sense that

$\text{lim}\text{→∞}\text{P}\text{sup}\text{0?s?t}\text{|P}{}_{\mathrm{A}}\text{(s) ? P(s)|>ε}\text{=0}\text{for every}\text{ε > 0}$

.In this paper, we obtain a “central limit theorem” for the random element √A(P_A(t)?P(t)). We prove that under appropriate conditions √A(P_A(t)?P(t)) will converge to a Gaussian process. (See Theorem 3.4 for the explicit formula of this Gaussian process.)     

Adaption of a fragment analysis technique to an automated high-throughput multicapillary electrophoresis device for the precise qualitative and quantitative characterization of microbial communities

The analysis of microbial communities is of increasing importance in life sciences and bioengineering. Traditional techniques of investigations like culture or cloning methods suffer from many disadvantages. They are unable to give a complete qualitative and quantitative view of the total amount of microorganisms themselves, their interactions among each other and with their environment. Obviously, the determination of static or dynamic balances among microorganisms is of fast growing interest. The generation of species specific and fluorescently labeled 16S ribosomal DNA (rDNA) fragments by the terminal restriction fragment length polymorphism (T-RFLP) technique is a suitable tool to overcome the problems other methods have. For the separation of these fragments polyacrylamide gel sequencers are preferred as compared to capillary sequencers using linear polymers until now because of their higher electrophoretic resolution and therefore sizing accuracy. But modern capillary sequencers, especially multicapillary sequencers, offer an advanced grade of automation and an increased throughput necessary for the investigation of complex communities in long-time studies. Therefore, we adapted a T-RFLP technique to an automated high-throughput multicapillary electrophoresis device (ABI 3100 Genetic Analysis) with regard to a precise qualitative and quantitative characterization of microbial communities.     

13 C 183W-Kopplungen als sonde für metall—carbin-, —carbenund—alkyl-bindungen

Carbon-13 NMR data are reported for trimethyltin derivatives containing ER_n groups where E  C, Si, Ge, Sn, N, O and S including a series of cyclic amines with ring sizes from three to seven. Coupling constant values for the homologous series of fourth group derivatives give goood correlations with the electronegativity of E. The observation of the two-bond, ¦ ²J(¹¹⁹SnE¹³C) ¦ couplings only in the derivatives containing bulky R groups is rationalized by a bimolecular exchange of ER_n groups in the concentrated solutions studied.     

The enthalpy of formation of magnesium sulfate ion pairs

The enthalpies of dilution of lithium, sodium, potassium, and magnesium chloride and sulfate solutions in the range 0.1 to 1.0 m have been measured at 30°C with a microcalorimeter. The relative apparent enthalpies φ_L of these solutions have been determined with the aid of an extended form of the Debye-Hückel limiting law $$\phi _L = S_H I^{1/2} [1/(1 + I^{1/2} ) - (\sigma /3)] + {\rm B}{\rm I} + CI^{3/2} $$ whereS _H is the limiting-law slope, σ = 3/I^3/2 × [(1+I^1/2 ? 1/(1+I^1/2 ? 2 ln (2+I^1/2)], andB andC are empirical constants. This equation fits the experimental results to within a standard deviation of 2 cal-mole^?1 for all the salts. The measured φ_L for the MgSO₄ solutions were compared to those calculated using the additivity principle, φ_L(MgCl₂) + φ_L(Na₂SO₄) ? 2φ_L(NaCl), and the extended Debye-Hückel equation. The results of this comparison have been used to calculate the ΔH _A ^o for the formation of MgSO ₄ ⁰ . A value of ΔH _A ^o = 1.15 to 1.36 was obtained, depending upon the φ_L estimates for the free ions Mg²⁺ and SO ₄ ^2? . The results are briefly discussed and compared to the results obtained by other workers.     

Metallorganische verbindungen der lanthanoide CVIII. Synthese und strukturaufklärung monomerer organolanthanoidacetate

LnCl₃ reacts with Na(C₅Me₄¹Bu) in THF to form the organolanthanoid chlorides [(C₅Me₄¹Bu)₂LnCl(THF)] (Ln = La (1a), Lu (1b)). Compounds 1a and 1b yield in reaction with NaO₂CCH₃ the monomeric organolanthanoid acetates [(C₅Me₄¹Bu)₂LnO₂CCH₃] (Ln = La (2a), Lu (2b)). The single crystal X-ray structure analysis of 2b as well as the cryoscopic molecular weight investigation of 2a verify the monomeric structure of these complexes.     

Determination of oxygen in alkali halide salts by proton activation and radiochemical separation

A lanthanum fluoride precipitation method for the separation of¹⁸F produced from the¹⁸O(p,n)¹⁸F reaction in alkali halide salts is described. This radiochemical separation method minimizes interferences from other positron emitters produced by proton bombardment and makes the accurate determination of ppm-level¹⁸O in complex alkali halide systems feasible. The interference from the¹⁹F(p,d)¹⁸F reaction is eliminated by keeping the proton energy less than 8.2 MeV. Applications of this technique to studies of dissolved oxide species in molten alkali halide salts are discussed.     

Dendrimeric organochalcogen catalysts for the activation of hydrogen peroxide: origins of the "dendrimer effect" with catalysts terminating in phenylseleno groups

Several scenarios were evaluated to explain the large "dendrimer effect" observed in the bromination of cyclohexene with H(2)O(2) and NaBr catalyzed by the addition of Frechét-type dendrimers terminating in -O(CH(2))(3)SePh groups. Although phenylseleninic acid was an efficient catalyst for the oxidation of NaBr with H(2)O(2), first-order rate constants for the selenoxide elimination were too small to produce PhSeO(2)H at a rate sufficient to explain the rates of catalysis and no dendrimer effect was observed in the rates of selenoxide elimination. An induction period was observed using 1-SePh as a catalyst for the oxidation of Br(-) with H(2)O(2). The addition of preformed selenoxide 1-Se(=O)Ph gave immediate catalysis with no induction period. However, rates of oxidation of the selenides with H(2)O(2) under homogeneous or biphasic conditions or with t-BuOOH under homogeneous conditions were too slow to account for the rates of catalysis, and no dendrimer effect was observed in the rates of oxidation. The primary oxidant for converting selenides to selenoxides was "Br(+)" produced initially by the uncatalyzed background reaction of H(2)O(2) with NaBr and then produced catalytically following formation of selenoxide groups. Autocatalysis is observed, and the rate of oxidation increases with the number of SePh groups. Autocatalysis is the source of the large dendrimer effect observed with the SePh series of catalysts.     

Solid-phase synthesis of lipidated peptides

Characteristic partial structures of lipidated proteins embodying different lipid groups as well as additional fluorescent tags or a maleimide for coupling to proteins can be synthesized readily by means of a new solid-phase technique employing the oxidative cleavage of the hydrazide linker as well as on-resin farnesylation and palmitoylation after appropriate deprotection of cysteine thiol groups as the key steps.