Gabor Frames in $${\ell }^2({\mathbb {Z}})$$ ℓ 2 ( Z ) and Linear Dependence

We prove that an overcomplete Gabor frame in \({\ell }^2({\mathbb {Z}})\) generated by a finitely supported sequence is always linearly dependent. This is a particular case of a general result about linear dependence versus independence for Gabor systems in \({\ell }^2({\mathbb {Z}})\) with modulation parameter 1 / M and translation parameter N for some \(M,N\in {\mathbb {N}},\) and generated by a finite sequence g in \({\ell }^2({\mathbb {Z}})\) with K nonzero entries.

     

Frame properties of systems arising via iterated actions of operators

Motivated by recent progress in dynamical sampling we prove that every frame which is norm-bounded below can be represented as a finite union of sequences ${\{{(T_j)}^n{\phi }_j\}}_{n=0}^{\infty },j=1,\dots ,J$ for some bounded operators $T_j$ and elements ${\phi }_j$ in the underlying Hilbert space. The result is optimal, in the sense that it turns out to be problematic to replace the collection of generators ${\phi }_1,\dots ,{\phi }_J$ by a singleton: indeed, for linearly independent frames we prove that we can represent the frame in terms of just one system ${\{T^n\phi \}}_{n=0}^{\infty }$, but unfortunately this representation often forces the operator T to be unbounded. Several examples illustrate the connection of the results to typical frames like Gabor frames and wavelet frames, as well as generic constructions in arbitrary separable Hilbert spaces.     

Topology optimization of 3D shell structures with porous infill

This paper presents a 3D topology optimization approach for designing shell structures with a porous or void interior. It is shown that the resulting structures are significantly more robust towards load perturbations than completely solid structures optimized under the same condi-tions. The study indicates that the potential benefit of using porous structures is higher for lower total volume fractions. Compared to earlier work dealing with 2D topology opti-mization, we found several new effects in 3D problems. Most notably, the opportunity for designing closed shells signifi-cantly improves the performance of porous structures due to the sandwich effect. Furthermore, the paper introduces improved filter boundary conditions to ensure a completely uniform coating thickness at the design domain boundary.     

Lipases,liposomes and lipid-prodrugs

Colloidal and interfacial phenomena lie at the core of drug formulation, drug delivery, as well as drug binding and action at diseased sites, e.g., in cancer therapy. We review a class of liposome-based drug-delivery systems whose design and functional properties are intimately controlled by the stability of sub-micron structures, lipid-bilayer interfaces, and interfacially activated enzymes that can be exploited to target and deliver drugs. Moreover these drugs can themselves be special lipid molecules in the form of lipid prodrugs that both form the liposomal carrier as well as the substrate for endogenously upregulated lipases that turn the prodrugs into potent drugs precisely at the diseased site.     

Probing Helical Hydrophobic Binding Sites in Branched Starch Polysaccharides Using NMR Spectroscopy

Branched starch polysaccharides are capable of binding multiple hydrophobic guests, but their exploitation as multivalent hosts and in functional materials is limited by their structural complexity and diversity. Linear α(1–4)‐linked glucose oligosaccharides are known to bind hydrophobic guests inside left‐handed single helices in solution and the solid state. Here, we describe the development of an amphiphilic probe that binds to linear α(1–4)‐linked glucose oligosaccharides and undergoes a conformational switch upon complexation, which gives rise to dramatic changes in the ¹H NMR spectrum of the probe. We use this probe to explore hydrophobic binding sites in the branched starch polysaccharides amylopectin and β‐limit dextrin. Diffusion‐ordered (DOSY), nuclear Overhauser effect (NOESY) and chemical shift perturbation (HSQC) NMR experiments are utilised to provide evidence that, in aqueous solution, branched polysaccharides bind hydrophobic guests in well‐defined helical binding sites, similar to those reported for complexation by linear oligosaccharides. By examining the binding affinity of the probe to systematically enzymatically degraded polysaccharides, we deduce that the binding sites for hydrophobic guests can be located on internal as well as external branches and that proximal α(1–6)‐linked branch points weaken but do not prevent complexation.     

Between Two Chairs: Combination of Theory and Experiment for the Determination of the Conformational Dynamics of Xylosides

The conformational properties of monosaccharides constitute fundamental features of oligosaccharides. While the energy landscape of monosaccharides can be altered by a specific biochemical environment or by chemical modifications, the analysis of resulting dynamic conformational equilibria is not feasible by experimental means alone. In this work, a series of β-d -xylopyranosides is used to outline how a combination of experimental NMR parameters and computed molecular properties can be used to determine conformers and quantify the composition of conformational equilibria. We demonstrate that identifying the most stable conformers using energy calculations is challenging and computing of NMR shieldings is typically not sensitive enough. On the other hand, computed spin-spin coupling constants for the xyloside ring can be used to unambiguously assign experimental NMR data of dynamic conformational equilibria and quantify the ratio of different conformers in the mixture. As a proof of principle, this procedure allowed to analyze a hitherto unknown dynamic equilibrium of a diamino-xyloside as a precursor of a molecular switch.     

Wet-Chemically Prepared Porphyrin Layers on Rutile TiO2(110)

Porphyrins are large organic molecules that are interesting for different applications, such as photovoltaic cells, gas sensors, or in catalysis. For many of these applications, the interactions between adsorbed molecules and surfaces play a crucial role. Studies of porphyrins on surfaces typically fall into one of two groups: (1) evaporation onto well-defined single-crystal surfaces under well-controlled ultrahigh vacuum conditions or (2) more application-oriented wet chemical deposition onto less well-defined high surface area surfaces under ambient conditions. In this study, we will investigate the wet chemical deposition of 5-(monocarboxyphenyl)-10,15,20-triphenylporphyrin (MCTPP) on well-defined rutile TiO₂(110) single crystals under ambient conditions. Prior to deposition, the TiO₂(110) crystals were also cleaned wet-chemically under ambient conditions, meaning none of the preparation steps were done in ultrahigh vacuum. However, after each preparation step, the surfaces were characterized in ultrahigh vacuum with X-ray photoelectron spectroscopy (XPS) and the result was compared with porphyrin layers prepared in ultrahigh vacuum (UHV) by evaporation. The differences of both preparations when exposed to zinc ion solutions will also be discussed.