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.

---

---

Herrn Prof. Dr. H.-J. Kanold zum 65. 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.)     

Trace lead measurement and on-line removal of matrix interference in seawater by isotope dilution coupled with flow injection and ICP-MS

Isotope dilution analysis method coupled with flow injection and inductively coupled plasma mass spectrometry (ID-FI-ICP-MS), enabled trace lead concentration in seawater to be determined and the high salt concentration in the matrix, such as Na⁺, Ca²⁺ and Mg²⁺, to be removed on-line. The operational parameters of the FI system including pH for the chelating reaction, concentration of 8-hydroxyquinoline-5-sulfonic acid (8-HQS), sample loading time and injection speed, washing time and speed, eluting acid concentration and eluting speed, and instrumental parameters for ICP-MS were optimized and selected. Accurate results could be achieved because the isotope ratios required can be precisely measured in the range of the eluting peak by means of ID-FI-ICP-MS. The 3σ detection limit was 0.204 ng ml⁻¹. The trace lead concentration of seawater in south Xiamen, China was 0.988 ± 0.039 ng ml⁻¹. The recoveries of spiked Pb standard in seawater and standard reference water (GBW 08607) were 97.9 and 101.0%, respectively, with a relative standard deviation of 0.98%. This method can be used to determine trace lead concentration in high salt matrix samples, and is especially useful when the eluting peaks do not have a Gaussian-distribution.     

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.     

Cell Cycle Kinetics Following UVA Irradiation in Comparison to UVB and UVC Irradiation

Abstract— There is limited information about the carcinogenic effect of longwave ultraviolet radiation (UVA: 315-400 nm). In particular very little is known about the relevant genotoxic damage caused by physiological doses of UVA radiation. A general response of cells to DNA damage is a delay or arrest of the cell cycle. Conversely, such cellular responses after UVA irradiation would indicate significant genotoxic damage. The aim of this study is to compare cell cycle kinetics of human fibroblasts after UVC (190-280 nm radiation), UVB (280-315 nm radiation) and UVA irradiation. Changes in the cell cycle kinetics were assessed by bivariate flow cytometric analysis of DNA synthesis and of DNA content. After UVC, UVB or UVA irradiation of human fibroblasts a suppression was seen of bromodeoxyuridine (BrdU) incorporation at all stages of S phase. The magnitude of this suppression appeared dose dependent. Maximum suppression was reached at 5-7 h after UVB exposure and directly after UVA exposure, and normal levels were reached 25 h after UVB and 7 h after UVA exposure. The lowered BrdU uptake corresponded with a lengthening of the S phase. No dramatic changes in percentages of cells in G₁, S and G₂/M were seen after the various UV irradiations. Apparently, UVA irradiation, like UVB and UVC irradiation, can temporarily inhibit DNA synthesis, which is indicative of genotoxic damage.     

Construction of triangular metallomacrocycles: [M3(1,2-bis(2,2':6',2''-terpyridin-4-yl-ethynyl)benzene)3][M = Ru(II), Fe(II), 2Ru(II)Fe(II)

Complexation of a predesigned (1,2-bis(2,2':6',2'-terpyridin-4-yl-ethynyl)benzene) ligand possessing a 60 degrees angle between two terpyridines with transition metals [Fe(II) and Ru(II)] afforded the self-assembled, triangular metallomacrocycles.     

Coordination Chemistry of Acrylamide: 1. Cobalt(II) Chloride Complexes with Acrylamide – Synthesis and Crystal Structures

The molecular structures of blue dichloro‐tetrakis(acrylamide) cobalt(II), [Co{O‐OC(NH₂)CH=CH₂}₄Cl₂] ( 1 ) and pink hexakis(acrylamide)cobalt(II) tetrachlorocobaltate(II), [Co{O‐OC‐(NH₂)CH=CH₂}₆][CoCl₄] ( 2 ), characterized by single X‐ray diffraction, IR spectroscopy and elemental analyses, are described. The coordination of Co^II in 1 involves a tetragonally distorted octahedral structure with four O‐donor atoms of acrylamide in the equatorial positions and two chloride ions in the apical positions. The second complex 2 in ionic form contains Co^II cations surrounded by an octahedral array of O‐coordinated acrylamide ligands, accompanied by a [CoCl₄]^2? anion.     

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.     

Measurement of PCDDs, PCDFs, and non-ortho-PCBs by comprehensive two-dimensional gas chromatography-isotope dilution time-of-flight mass spectrometry (GC x GC-IDTOFMS)

Comprehensive two-dimensional gas chromatography with isotope-dilution time-of-flight mass spectrometry (GC × GC-IDTOFMS) was used to measure polychlorinated dibenzo-p-dioxin (PCDD), polychlorinated dibenzofuran (PCDF), and coplanar polychlorinated biphenyl (cPCB) concentrations in ash, sediment, vegetation, and fish samples. The GC × GC capability was achieved by using a quad jet, dual stage, thermal modulator. Zone compression of the GC peaks from modulation resulted in a significant increase of the signal intensity over classical GC-IDTOFMS. The GC × GC column set used an Rtx-Dioxin 2 phase as the first dimension (¹D) and an Rtx-500 as the second dimension (²D). The chromatographic separation of the 17 PCDD/Fs and the 4 cPCBs was attained in ¹D except for 2,3,7,8-TCDD and CB126 for which deconvoluted ion currents (DIC) were required to be reported separately. The Rtx-500 phase separated the bulk matrix interfering compounds from the target analytes in ²D. The instrumental limit of detection (iLODs) was 0.5 pg for 2,3,7,8-TCDD. The calibration curves showed good correlation coefficients for all the compounds investigated in the concentration range of 0.5–200 pg. GC × GC-IDTOFMS results compared favorably to those from conventional isotope-dilution one-dimensional gas chromatography-high resolution mass spectrometry (GC-IDHRMS). The comprehensive mass analysis of the TOFMS further permitted the identification of other contaminants of concern in the samples.