A Decay Result for Certain Windows Generating Orthogonal Gabor Bases

We consider tight Gabor frames (h,a=1,b=1) at critical density with h of the form Z ⁻¹(Zg/|Zg|). Here Z is the standard Zak transform and g is an even, real, well-behaved window such that Zg has exactly one zero, at , in [0,1)². We show that h and its Fourier transform have maximal decay as allowed by the Balian-Low theorem. Our result illustrates a theorem of Benedetto, Czaja, Gadziński, and Powell, case p=q=2, on sharpness of the Balian-Low theorem.      

Infinite Random Geometric Graphs

We introduce a new class of countably infinite random geometric graphs, whose vertices V are points in a metric space, and vertices are adjacent independently with probability p ? (0, 1){p \in (0, 1)} if the metric distance between the vertices is below a given threshold. For certain choices of V as a countable dense set in \mathbbRⁿ{\mathbb{R}^n} equipped with the metric derived from the L _∞-norm, it is shown that with probability 1 such infinite random geometric graphs have a unique isomorphism type. The isomorphism type, which we call GR _n , is characterized by a geometric analogue of the existentially closed adjacency property, and we give a deterministic construction of GR _n . In contrast, we show that infinite random geometric graphs in \mathbbR²{\mathbb{R}^{2}} with the Euclidean metric are not necessarily isomorphic.     

Biased Diffusion with Correlated Noise

The diffusion of hard-core particles subject to a global bias is described by a nonlinear, anisotropic generalization of the diffusion equation with conserved, local noise. Using renormalization group techniques, we analyze the effect of an additional noise term, with spatially long-ranged correlations, on the long-time, long-wavelength behavior of this model. Above an upper critical dimension d _LR, the long-ranged noise is always relevant. In contrast, for d<d _LR, we find a weak noise regime dominated by short-range noise. As the range of the noise correlations increases, an intricate sequence of stability exchanges between different fixed points of the renormalization group occurs. Both smooth and discontinuous crossovers between the associated universality classes are observed, reflected in the scaling exponents. We discuss the necessary techniques in some detail since they are applicable to a much wider range of problems.     

Identification and quantification of polycarboxylates in detergent products using off-line size exclusion chromatography-nuclear magnetic resonance

The performance of many contemporary detergent products critically depends on polymers. Water-soluble polycarboxylates represent an important class of detergent polymers, and their quantitative assessment in detergent matrices stands as a considerable challenge. The presence of high levels of surfactants is a major complication, due to the strong tendency of surfactants to form micelles and to interact with the polymers. First, we addressed critical steps in the subsequent combined use of liquid extraction and off-line size exclusion chromatography-nuclear magnetic resonance (SEC-NMR) for identification and quantification of polycarboxylates in detergent products. Next, the different steps in the off-line SEC-NMR procedure were optimized with respect to precision and accuracy. This resulted in recoveries of more than 80% for maleic acid/acrylic acid copolymers; in detergent products a proportional bias of 30% is achieved. The method showed good precision with a relative standard deviation of within-laboratory reproducibility between 5% and 14%.     

The Effect of α-Branched Side Chains on the Structural and Opto-Electronic Properties of Poly(Diketopyrrolopyrrole-alt-Terthiophene)

Introducing solubilizing α-branched alkyl chains on a poly(diketopyrrolopyrrole-alt-terthiophene) results in a dramatic change of the structural, optical, and electronic properties compared to the isomeric polymer carrying β-branched alkyl side chains. When branched at the α-position the alkyl substituent creates a steric hindrance that reduces the tendency of the polymer to π–π stack and endows the material with a much higher solubility in common organic solvents. The wider π–π stacking and reduced tendency to crystallize, evidenced from grazing-incidence wide-angle X-ray scattering, result in a wider optical band gap in the solid state. In solar cells with a fullerene acceptor, the α-branched isomer affords a higher open-circuit voltage, but an overall lower power conversion efficiency as a result of a too well-mixed nanomorphology. Due its reduced π–π stacking, the α-branched isomer fluoresces and affords near-infrared light-emitting diodes emitting at 820 nm.     

Formation of boldenone and boldenone-analogues by maggots of Lucilia sericata

Current evidence suggests that neo formation of the anabolic steroid boldenone (androsta-1,4-diene-17-ol-3-one) occurs in calves' faecal material, making it difficult to distinguish between illegally administered boldenone and its potential endogenous presence. This strengthens the urgent need to elucidate the pathway leading to boldenone formation. In our laboratory, the invertebrate Neomysis integer (Crustacea, Mysidacea) was used since 2004 as an alternative model for the partial replacement of vertebrate animals in metabolisation studies with illegal growth promotors and veterinary drugs, e.g. boldenone. The present study evaluates the metabolic capacity of other invertebrates, the brine shrimp Artemia franciscana and maggots of the greenbottle fly Lucilia sericata. The first results indicate that maggots of L. sericata are able to convert phytosterols and -stanols, nowadays in substantial amounts added to animal feed, into androsta-1,4-diene-3,17-dione (ADD), the precursor of boldenone, at a yield of 0.10-0.14% (p<0.001, significance compared to endogenous excretion of maggots) but not to boldenone itself. Furthermore, beta-testosterone, an endogenous hormone, was transformed into androst-4-ene-3,17-dione (AED), ADD and beta-boldenone at a significant (p<0.001, significance compared to endogenous excretion of maggots) yield of circa 13%, 0.80% and 2.2%, respectively. In future studies these results are of value to further evaluate the use of maggots of L. sericata as an invertebrate model in metabolisation studies.     

A new method for the automated selection of the number of components for deconvolving overlapping chromatographic peaks

Mathematical deconvolution methods can separate co-eluting peaks in samples for which (chromatographic) separation fail. However, these methods often heavily rely on manual user-input and interpretation. This is not only time-consuming but also error-prone and automation is needed if such methods are to be applied in a routine manner.