Existence of non-trivial harmonic functions on Cartan–Hadamard manifolds of unbounded curvature

The Liouville property of a complete Riemannian manifold M (i.e., the question whether there exist non-trivial bounded harmonic functions on M) attracted a lot of attention. For Cartan–Hadamard manifolds the role of lower curvature bounds is still an open problem. We discuss examples of Cartan–Hadamard manifolds of unbounded curvature where the limiting angle of Brownian motion degenerates to a single point on the sphere at infinity, but where nevertheless the space of bounded harmonic functions is as rich as in the non-degenerate case. To see the full boundary the point at infinity has to be blown up in a non-trivial way. Such examples indicate that the situation concerning the famous conjecture of Greene and Wu about existence of non-trivial bounded harmonic functions on Cartan–Hadamard manifolds is much more complicated than one might have expected.      

Air-Initiated Radical Polymerization of Lithium Salts of omega-(Undecamethylcarba-closo-dodecaboran-1'-yl)alk-1-enes, CH2=CH(CH2)(n-2)C(BMe)11- Li+

We report an easy access to the salts of the LiC(BMe)11- anion, which greatly simplifies the synthesis of compounds carrying the -C(BMe)11- substituent, including the title anions. The previously recognized and puzzling spontaneous oligomerization of the solid lithium salts CH2=CH(CH2)(n-2)C(BMe)11- Li+ upon storage under ambient conditions is now shown to proceed by a radical mechanism, with the "naked" Li+ cation acting as a catalyst. The degree of polymerization is higher in solution, especially when azoisobutyronitrile (AIBN) is used as initiator (up to approximately 50). Initiation by the thermal decomposition of AIBN is also catalyzed by naked Li+, and this initiator is effective at room temperature. Di-tert-butyl peroxide and UV irradiation can also be used. The observation of Li+ catalysis agrees with a prior prediction from ab initio calculations, according to which Li+ complexation of ethylene strongly lowers the activation energy for methyl radical addition. The results bear on the current discussion of the possible sensitivity of radical clocks to their molecular environment and suggest that naked Li+ will catalyze the radical polymerization of simple terminal alkenes.     

Illuminating the BOLD signal: combined fMRI-fNIRS studies

Functional magnetic resonance imaging (fMRI) is currently combined with electrophysiological methods to identify the relationship between neuronal activity and the blood oxygenation level-dependent (BOLD) signal. Several processes like neuronal activity, synaptic activity, vascular dilation, blood volume and oxygenation changes underlie both response modalities, that is, the electrophysiological signal and the vascular response. However, accessing single process relationships is absolutely mandatory when aiming at a deeper understanding of neurovascular coupling and necessitates studies on the individual building blocks of the vascular response. Combined fMRI and functional near-infrared spectroscopy studies have been performed to validate the correlation of the BOLD signal to the hemodynamic changes in the brain. Here we review the current status of the integration of both technologies and judge these studies in the light of recent findings on neurovascular coupling.     

Topology Optimization of 3D Elastic Structures Using Boundary Elements

A numerical approach for the topological optimization of 3D linear elastic problems using boundary elements and the topological derivative is presented in this work. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Improved Thin‐Film Transistor Performance Through a Melt of Poly(para‐phenyleneethynylene)

The performance of polymer field‐effect transistors (PFETs) based on short rigid rod semiconducting poly(2,5‐didodecyloxy‐p‐phenyleneethynylene) (D‐OPPE) is highlighted. The controlled heating and cooling of thin films of D‐OPPE allows for a recrystallization from the melt, boosting the performance of D‐OPPE‐based transistors. The improved film properties induced by controlled annealing lead to a hole field‐effect mobility around 0.014 cm² V⁻¹ s⁻¹, an on/off ratio of 10⁶, a sub‐threshold swing of 3 V dec⁻¹ and a threshold voltage of −35 V, employing a poly(methyl methacrylate) (PMMA) gate dielectric. Thus, PFETs out of D‐OPPE compete now with spin‐coated, polycrystalline poly(3‐hexylthiophene)‐based PFETs.

     

Synthesis and Crystal Structure of a New Salt of the Water‐Stable Hexathiohypodiphosphate Anion: [py2Li]4[P2S6] ·2 py

A new rare example of a synthetic route in solution to the hexathiohypodiphosphate anion P₂S₆⁴⁻ is presented. Starting from P₄S₃, Li₂S, and elemental sulfur in pyridine, this reaction yields yellow block‐shaped crystals of [py₂Li]₄[P₂S₆] · 2 py ( 1 ). The molecular structure of this hitherto unknown compound was determined by single crystal X‐ray diffraction and reveals a heteronorbornane skeleton within the Li₄P₂S₆ entity.     

Increments to chiral recognition facilitating enantiomer separations of chiral acids, bases, and ampholytes using Cinchona-based zwitterion exchanger chiral stationary phases

The intramolecular distances of anion and cation exchanger sites of zwitterionic chiral stationary phases represent potential tuning sites for enantiomer selectivity. In this contribution, we investigate the influence of alkanesulfonic acid chain length and flexibility on enantiomer separations of chiral acids, bases, and amphoteric molecules for six Cinchona alkaloid-based chiral stationary phases in comparison with structurally related anion and cation exchangers. Employing polar-organic elution conditions, we observed an intramolecular counterion effect for acidic analytes which led to reduced retention times but did not impair enantiomer selectivities. Retention of amphoteric analytes is based on simultaneous double ion pairing of their charged functional groups with the acidic and basic sites of the zwitterionic selectors. A chiral center in the vicinity of the strong cation exchanger site is vital for chiral separations of bases. Sterically demanding side chains are beneficial for separations of free amino acids. Enantioseparations of free (un-derivatized) peptides were particularly successful in stationary phases with straight-chain alkanesulfonic acid sites, pointing to a beneficial influence of more flexible moieties. In addition, we observed pseudo-enantiomeric behavior of quinine and quinidine-derived chiral stationary phases facilitating reversal of elution orders for all analytes.     

Hydrangenone, a new isoprenoid with an unprecedented skeleton from Salvia hydrangea

Hydrangenone, a new heptacyclic isoprenoid with a 6/7/6/5/5 membered carbon ring skeleton, was isolated from the aerial parts of Salvia hydrangea. The structure was established by extensive NMR spectroscopic methods. The relative and absolute configuration of 1 was assigned by NOESY and X-ray crystallographic analysis and by comparison of experimental and calculated electronic circular dichroism (ECD) spectra. Compound 1 showed in vitro antiplasmodial activity, with an IC(50) value of 1.4 μM against P. falciparum. A plausible biosynthetic pathway of 1 was also proposed.