On Inhomogeneous Diophantine Approximations with Rational Terms and Applications to Elliptic and Trigonometric Functions

We investigate inhomogeneous diophantine approximation problems of the type ¦qθ ? p t- α¦. Lower bounds for the error terms are proved in the case of arbitrarily chosen rational α’s. Applications are given to elliptic and trigonometric functions extending former results of the author and others.     

Carbon and nitrogen isotope analysis of atrazine and desethylatrazine at sub-microgram per liter concentrations in groundwater

Environmental degradation of organic micropollutants is difficult to monitor due to their diffuse and ubiquitous input. Current approaches—concentration measurements over time, or daughter-to-parent compound ratios—may fall short, because they do not consider dilution, compound-specific sorption characteristics or alternative degradation pathways. Compound-specific isotope analysis (CSIA) offers an alternative approach based on evidence from isotope values. Until now, however, the relatively high limits for precise isotope analysis by gas chromatography—isotope ratio mass spectrometry (GC-IRMS) have impeded CSIA of sub-microgram-per-liter scale micropollutant concentrations in field samples. This study presents the first measurements of C and N isotope ratios of the herbicide atrazine and its metabolite desethylatrazine at concentrations of 100 to 1,000 ng/L in natural groundwater samples. Solid-phase extraction and preparative HPLC were tested and validated for preconcentration and cleanup of groundwater samples of up to 10 L without bias by isotope effects. Matrix interferences after solid-phase extraction could be greatly reduced by a preparative HPLC cleanup step prior to GC-IRMS analysis. Sensitivity was increased by a factor of 6 to 8 by changing the injection method from large-volume to cold-on-column injection on the GC-IRMS system. Carbon and nitrogen isotope values of field samples showed no obvious correlation with concentrations or desethylatrazine-to-atrazine ratios. Contrary to expectations, however, δ ¹³ C values of desethylatrazine were consistently less negative than those of atrazine from the same sites. Potentially, this line of evidence may contain information about further desethylatrazine degradation. In such a case, the common practice of using desethylatrazine-to-atrazine ratios would underestimate natural atrazine degradation.     

Measurement of the electric form factor of the neutron at Q2 = 0.3-0.8 (GeV/ c) 2 ⋆

The electric form factor of the neutron, G_E,n, has been measured at the Mainz Microtron by recoil polarimetry in the quasielastic D(¯e, e¯n)p reaction. Three data points have been extracted at squared four-momentum transfers Q ² = 0.3, 0.6 and 0.8 (GeV/c)². Corrections for nuclear binding effects have been applied.This revised version was published online in March 2005. In the previous version, the email address of one author was inadvertently assigned to multiple authors.     

On a universal differential equation for the analytic terms of C-superpositions on the real line

It is proved that every continuous function on the real line can be approximated uniformly (in the sense of a specific norm) by superpositions of analytic functions, which are solutions of a single universal differential equation. Every superposition is some function belonging to . This improves a former result of the author, from which the superpositions are known to be continuous.