The Kolmogorov–Riesz compactness theorem

We show that the Arzelà–Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their relation to Helly's theorem is discussed. The paper contains a detailed discussion on the historical background of the Kolmogorov compactness theorem.     

13C-Leucin-Atemtest zur Beurteilung der anabolen Verwertung von diätetischen Aminosäurengemischen bei Phenylketonurie

It is essential to establish whether and how environmental factors affect the reliability of [¹³C]methacetin breath test (¹³C-MBT). In 12 healthy volunteers (smokers), a standard ¹³C-MBT with 75 mg [¹³C]methacetin was performed twice in random order: on a control day without smoking and on another day with smoking two cigarettes antecedently. A considerable flattening of the curve of the momentary ¹³C recovery within the expiratory air was observed when the ¹³C-MBT was performed after smoking. The maximum of the momentary ¹³C recovery, D _max, decreased from 37.20±2.58 to 25.39±2.29% dose/h (p=0.00052). Moreover, the time to reach D _max was prolonged after cigarette smoking (26.5±3.1 vs. 16.5±1.9 min, p=0.0199). The curve of the cumulative ¹³C recovery on the cigarette smoking day appeared to be shifted downwards, and statistically significant differences relative to the control situation were found between the 24th and 75th minute following [¹³C]methacetin administration. Smoking cigarettes immediately prior to the ¹³C-MBT diminishes the ability of the liver to handle methacetin, and hence a possibility of such an interaction should be excluded in order to interpret the results of the test correctly.     

Reversible Optical Writing and Data Storage in an Anthracene‐Loaded Metal–Organic Framework

Metal–organic frameworks (MOFs) enable the design of host–guest systems with specific properties. In this work, we show how the confinement of anthracene in a well‐chosen MOF host leads to reversible yellow‐to‐purple photoswitching of the fluorescence emission. This behavior has not been observed before for anthracene, either in pure form or adsorbed in other porous hosts. The photoresponse of the host–guest system is caused by the photodimerization of anthracene, which is greatly facilitated by the pore geometry, connectivity, and volume as well as the structural flexibility of the MOF host. The photoswitching behavior was used to fabricate photopatternable and erasable surfaces that, in combination with data encryption and decryption, hold promise in product authentication and secure communication applications.     

Quasi-one-dimensional magnetism driven by unusual orbital ordering in CuSb2O6

Essentially all undoped cuprates exhibit a quasiplanar, fourfold Cu-O coordination responsible for the magnetically active antibonding 3d(x(2)-y(2)) like state. Here, we present an electronic structure study for CuSb(2)O(6) that reveals, in contrast, a half-filled 3d(3z(2)-r(2)) orbital. This hitherto unobserved ground state originates from a competition of in- and out-of-plaquette orbitals where the strong Coulomb repulsion drives the surprising and unique orbital ordering. This, in turn, gives rise to an unexpected quasi-one-dimensional magnetic behavior. Our results provide a consistent explanation of recent thermodynamical and neutron diffraction measurements.     

Submicron gold structures formed by atomic force microscopy lithography on thin films of poly(methyl methacrylate)

Thin films of poly(methyl methacrylate) (PMMA) (25 nm) deposited on gold coated glass substrates have been locally modified by exposure to biased atomic force microscopy (AFM) tips. Constant exposure currents in the range of 0.5–0.65 nA leads to removal of PMMA both by direct ablation and enhanced solubility in a developer solution. Possible mechanisms causing such modifications have been discussed. Submicron Au structures were formed by combining AFM lithography, involving localized removal of PMMA, with sputter deposition of gold and a lift-off process.     

A Ferrocenyl Kaleidoscope: Slow Interconversion of Six Diastereo‐atropisomers of 2,6‐Di‐tert‐butyl‐9,10‐diferrocenyltriptycene

The title triptycene, 6 , has been isolated as the product of 9,10‐cycloaddition of benzyne to 9,10‐diferrocenyl‐2,6‐di‐tert‐butylanthracene, 5 , whose X‐ray crystal structure is reported. Each ferrocenyl unit in 6 has access to the same three non‐equivalent molecular environments, and their rotations relative to the molecular paddlewheel give rise to six slowly interconverting atropisomers. Their dynamic behaviour in solution is a challenging NMR puzzle that can be successfully solved by taking advantage of the recently described very large diamagnetic anisotropy of the ferrocenyl moiety, together with the C₂ symmetry of particular atropisomers. Application of one‐ and two‐dimensional NMR techniques over a range of temperatures together, with a detailed analysis of the homo‐ and heteronuclear correlations in 6 , resulted in unequivocal mapping of the 99 ¹H and 162 ¹³C positions in the six interconverting systems. Variable‐temperature 2D‐EXSY measurements revealed that, while the stability of the atropisomers is almost identical, they are separated by energy barriers which the ferrocenyls must overcome in the course of their interconversions. The heights of two different rotational barriers have been identified and these experimental findings are in good agreement with DFT calculations.     

Type S Non-Ribosomal Peptide Synthetases for the Rapid Generation of Tailormade Peptide Libraries**

Bacterial natural products in general, and non-ribosomally synthesized peptides in particular, are structurally diverse and provide us with a broad range of pharmaceutically relevant bioactivities. Yet, traditional natural product research suffers from rediscovering the same scaffolds and has been stigmatized as inefficient, time-, labour- and cost-intensive. Combinatorial chemistry, on the other hand, can produce new molecules in greater numbers, cheaper and in less time than traditional natural product discovery, but also fails to meet current medical needs due to the limited biologically relevant chemical space that can be addressed. Consequently, methods for the high throughput generation of new natural products would offer a new approach to identifying novel bioactive chemical entities for the hit to lead phase of drug discovery programs. As a follow-up to our previously published proof-of-principle study on generating bipartite type S non-ribosomal peptide synthetases (NRPSs), we now envisaged the de novo generation of non-ribosomal peptides (NRPs) on an unreached scale. Using synthetic zippers, we split NRPSs in up to three subunits and rapidly generated different bi- and tripartite NRPS libraries to produce 49 peptides, peptide derivatives, and de novo peptides at good titres up to 145 mg L⁻¹. A further advantage of type S NRPSs not only is the possibility to easily expand the created libraries by re-using previously created type S NRPS, but that functions of individual domains as well as domain-domain interactions can be studied and assigned rapidly.