Necessary and sufficient conditions for convergence of regularization methods for solving linear operator equations of the first kind

In this paper, we give necessary and sufficient conditions for weak and strong convergence of general regularization methods for the solution of linear ill-posed problems in Hilbert space. As special cases we obtain convergence criteria for Tychonoff regularization, for a regularization method based on Showalter's integral formula, and for regularization by truncated iteration     

Assessment of commutability for candidate certified reference material ERM-BB130 “chloramphenicol in pork”

Chloramphenicol (CAP), an effective antibiotic against many microorganisms, is meanwhile banned in the EU for treatment of food-producing animals due to adverse health effects. The Institute for Reference Materials and Measurements (IRMM) is currently developing a certified reference material (CRM) for CAP in pork, intended for validation and method performance verifications of analytical methods. The material will be certified using liquid chromatography–tandem mass spectrometry (LC–MS/MS) and gas chromatography–mass spectrometry (GC–MS) methods and has a target CAP level around the minimum required performance limit (MRPL) of 0.3 μg/kg. To prove that the material can be applied as a quality control tool for screening methods, a commutability study was conducted, involving five commercially available enzyme-linked immunosorbent assay kits and one biosensor assay (BiaCore kit). Meat homogenates (cryo-milled wet tissue) with CAP concentrations around the MRPL and the candidate CRM (lyophilised powder) were measured by LC–MS/MS and GC–MS as well as the six screening methods. Pairwise method comparisons of results obtained for the two sample types showed that the CRM can successfully be applied as quality control (QC) sample to all six screening methods. The study suggests that ERM-BB130 is sufficiently commutable with the investigated assays and that laboratories applying one of the investigated kits therefore benefit from using ERM-BB130 to demonstrate the correctness of their results. However, differences among the assays were observed, either in the abundance of bias between screening and confirmatory LC and GC methods, the repeatability of test results, or goodness of fit between the methods.     

An Improved Cauchy Formula for Hypermonogenic Functions

A new Cauchy-type formula for hypermonogenic functions is derived. Hypermonogenic functions, introduced in [6], are a generalization of holomorphic functions to several dimensions. The power function x^m is hypermonogenic. This paper is dedicated to the memory of our friend and colleague Jarolim Bureš     

Intramolecular nucleophilic capture of radical cations by tethered hydroxy functions

A range of systems bearing hydroxy functions tethered to the molecular framework gives rise to a family of interesting radical cations, 5⁺-11⁺, upon electron transfer to photo-excited cyanoaromatics. Geraniol (5), nerol (6), citronellol (7), chrysanthemol (8), homochrysanthemol (9), trans-1-o-hydroxyphenyl-2-phenylcyclopropane (10), and endo-5-hydroxymethylnorbornene (11), generate a series of mono-, bi-, or tricyclic ethers via a series of four- to seven-membered transition states. Two of the radical cations, 5⁺ and 6⁺, undergo tandem cyclizations where 1,5- and/or 1,6-C-C cyclizations precede nucleophilic capture.     

Tandem mass spectrometric analysis of a complex triterpene saponin mixture of Chenopodium quinoa

A nano-HPLC electrospray ionization multi-stage tandem mass spectrometry (nLC-ESI-MS/MS) approach was applied to a complex crude triterpene saponin extract of Chenopodium quinoa seed coats. In ESI-MS/MS spectra of triterpene saponins, characteristic fragmentation reactions are observed and allow the determination of aglycones, saccharide sequences, compositions, and branching. Fragmentation of aglycones provided further structural information. The chemical complexity of the mixture was resolved by a complete profiling. Eighty-seven triterpene saponins comprising 19 reported and 68 novel components were identified and studied by MS. In addition to four reported, five novel triterpene aglycones were detected and characterized according to their fragmentation reactions in ESI-MS/MS and electron ionization mass spectrometry (EI-MS). As a novelty fragmentation pathways were proposed and analyzed based upon quantum chemical calculations using a hybrid Hartree-Fock density functional method. Accuracy of the assignment procedure was proven by isolation and structure determination of a novel compound. As the relative distribution and composition of saponins varies between different cultivars and soils, the presented strategy allows a rapid and complete analysis of Chenopodium quinoa saponin distribution and composition, and is particularly suitable for quality control and screening of extracts designated for pharmaceutical, agricultural, and industrial applications.     

On the biosynthetic origin of methoxymalonyl-acyl carrier protein, the substrate for incorporation of "glycolate" units into ansamitocin and soraphen A

Feeding experiments with isotope-labeled precursors rule out hydroxypyruvate and TCA cycle intermediates as the metabolic source of methoxymalonyl-ACP, the substrate for incorporation of "glycolate" units into ansamitocin P-3, soraphen A, and other antibiotics. They point to 1,3-bisphosphoglycerate as the source of the methoxymalonyl moiety and show that its C-1 gives rise to the thioester carbonyl group (and hence C-1 of the "glycolate" unit), and its C-3 becomes the free carboxyl group of methoxymalonyl-ACP, which is lost in the subsequent Claisen condensation on the type I modular polyketide synthases (PKS). d-[1,2-(13)C(2)]Glycerate is also incorporated specifically into the "glycolate" units of soraphen A, but not of ansamitocin P-3, suggesting differences in the ability of the producing organisms to activate glycerate. A biosynthetic pathway from 1,3-bisphosphoglycerate to methoxymalonyl-ACP is proposed. Two new syntheses of R- and S-[1,2-(13)C(2)]glycerol were developed as part of this work.     

K isomers in 254No: probing single-particle energies and pairing strengths in the heaviest nuclei

We have identified two isomers in 254No, built on two- and four-quasiparticle excitations, with quantum numbers K pi = 8- and (14+), as well as a low-energy 2-quasiparticle Kpi = 3+ state. The occurrence of isomers establishes that K is a good quantum number and therefore that the nucleus has an axial prolate shape. The 2-quasiparticle states probe the energies of the proton levels that govern the stability of superheavy nuclei, test 2-quasiparticle energies from theory, and thereby check their predictions of magic gaps.     

LC–high resolution MS in environmental analysis: from target screening to the identification of unknowns

This article provides an overview of the state-of-the-art and future trends of the application of LC–high resolution mass spectrometry to the environmental analysis of polar micropollutants. Highly resolved and accurate hybrid tandem mass spectrometry such as quadrupole/time-of-flight and linear ion trap/orbitrap technology allows for a more reliable target analysis with reference standards, a screening for suspected analytes without reference standards, and a screening for unknowns. A reliable identification requires both high resolving power and high mass spectral accuracy to increase selectivity against the matrix background and for a correct molecular formula assignment to unknown compounds. For the identification and structure elucidation of unknown compounds within a reasonable time frame and with a reasonable soundness, advanced automated software solutions as well as improved prediction systems for theoretical fragmentation patterns, retention times, and ionization behavior are needed.     

Towards future reference systems for GM analysis

Despite the fact that the measurement unit for the quantification of GMOs in food and feed products has not yet been unambiguously agreed upon in Europe, international trade requires reliable GMO analysis measuring comparably the GMO content of products. The two reference systems, based either on mass fractions or on copy number ratios, and their metrological traceability chains are presented and discussed. It is concluded that, properly established and expressed, measurement results in copy number ratios can provide a metrologically sound reference system. In this case, certified reference materials used for calibration and quality control can be independent of each other and the uncertainty derived from calibration can correctly be included in the overall uncertainty of the GMO measurement. However, further efforts are required to establish this metrological system.