Phase Retrieval from 4N−4 Measurements: A Proof for Injectivity

We prove by means of elementary methods that phase retrieval of complex polynomials p of degree less than N is possible with 4N − 4 phaseless Fourier measurements of p and p′. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis and characterization of polymer linked copper(I) bis(N‐heterocyclic carbene) mechanocatalysts

In this paper, the synthesis and characterization of a series of latent polymeric bis(N‐heterocyclic carbene) (NHC) copper(I) complexes is reported, which can be activated for the copper(I)‐catalyzed azide/alkyne cycloaddition (CuAAC) via ultrasound. To prove the influence of chain length and nature of the polymer towards the activation, poly(isobutylene) (PIB), poly(styrene) (PS) and poly(tetrahydrofuran) (PTHF) are synthesized via living polymerization techniques (LCCP, ATRP, CROP) obtaining different chain lengths (from 2500 to 9000 g/mol), followed by quaternization with N‐methylimidazole, generating the corresponding N‐methylimidazolium‐telechelic polymers. The deprotonation of these macroligands via strong bases like sodium tert‐butoxide (NaO^tBu) or potassium hexamethyldisilazide (KHMDS) yields the free N‐heterocyclic carbenes (NHCs), which are used to coordinate to tetrakis(acetonitrile)copper(I) hexafluorophosphate, forming the final polymer‐based mono‐ and bis(N‐methylimidazole‐2‐ylidene) copper(I)X complexes. The structural proof of these complexes is accomplished via ¹H‐NMR spectroscopy, MALDI‐TOF‐MS and GPC‐techniques. The activation of the copper(I) biscarbene catalysts by ultrasound is studied by GPC, revealing the cleavage of one shielding NHC‐ligand. The initial catalytic latency and the via ultrasound introduced catalytic activation is successfully demonstrated monitoring a CuAAC “click” reaction of benzyl azide and phenylacetylene by in situ ¹H‐NMR spectroscopy introducing thus “click” conversions up to 97%. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 3893–3907     

Precession and Interference in the Aharonov–Casher and Scalar Aharonov–Bohm Effects

The ideal scalar Aharonov–Bohm (SAB) and Aharonov–Casher (AC) effect involve a magnetic dipole pointing in a certain fixed direction: along a purely time dependent magnetic field in the SAB case and perpendicular to a planar static electric field in the AC case. We extend these effects to arbitrary direction of the magnetic dipole. The precise conditions for having nondispersive precession and interference effects in these generalized set ups are delineated both classically and quantally. Under these conditions the dipole is affected by a nonvanishing torque that causes pure precession around the directions defined by the ideal set ups. It is shown that the precession angles are in the quantal case linearly related to the ideal phase differences, and that the nonideal phase differences are nonlinearly related to the ideal phase differences. It is argued that the latter nonlinearity is due to the appearance of a geometric phase associated with the nontrivial spin path. It is further demonstrated that the spatial force vanishes in all cases except in the classical treatment of the nonideal AC set up, where the occurring force has to be compensated by the experimental arrangement. Finally, for a closed space-time loop the local precession effects can be inferred from the interference pattern characterized by the nonideal phase differences and the visibilities. It is argued that this makes it natural to regard SAB and AC as essentially local and nontopological effects.     

Development of reference materials for microbiological analysis

The reliability of reference materials (RMs) depends on properties such as fitness, robustness, commutability, stability and homogeneity. The development of RMs for microbiological analysis is especially challenged through questions around the stabilisation and recovery of viable cells, the dispersion of precise numbers of cells, matrix effects and, when using molecular techniques, the presence of nucleic acids (e.g. DNA) of dead and live target organisms. However, RMs are indispensable tools for quality control in microbiological analysis. The Institute for Reference Materials and Measurements (IRMM), as part of the European Commission, concentrates its efforts on the development of RMs to support the development, implementation and monitoring of EU legislation. A special focus is given to highly precise RMs for presence/absence and enumeration tests in microbiological food and water analysis. Another group of new RMs certified by the IRMM comprise DNA-based materials to control the identity of micro-organisms in qualitative assays. All of these activities serve to improve quality control in microbiological analysis. Presented at ‘BERM-10’, April 2006, Charleston, SC, USA.