Improved linear multi-step methods for stochastic ordinary differential equations

We consider linear multi-step methods for stochastic ordinary differential equations and study their convergence properties for problems with small noise or additive noise. We present schemes where the drift part is approximated by well-known methods for deterministic ordinary differential equations. In previous work, we considered Maruyama-type schemes, where only the increments of the driving Wiener process are used to discretize the diffusion part. Here, we suggest the improvement of the discretization of the diffusion part by also taking into account mixed classical-stochastic integrals. We show that the relation of the applied step sizes to the smallness of the noise is essential in deciding whether the new methods are worthwhile. Simulation results illustrate the theoretical findings.     

Isolation of Elusive HAsAsH in a Crystalline Diuranium(IV) Complex

The HAsAsH molecule has hitherto only been proposed tentatively as a short‐lived species generated in electrochemical or microwave‐plasma experiments. After two centuries of inconclusive or disproven claims of HAsAsH formation in the condensed phase, we report the isolation and structural authentication of HAsAsH in the diuranium(IV) complex [{U(Tren^TIPS)}₂(μ‐η²:η²‐As₂H₂)] ( 3 , Tren^TIPS=N(CH₂CH₂NSiPrⁱ₃)₃; Prⁱ=CH(CH₃)₂). Complex 3 was prepared by deprotonation and oxidative homocoupling of an arsenide precursor. Characterization and computational data are consistent with back‐bonding‐type interactions from uranium to the HAsAsH π*‐orbital. This experimentally confirms the theoretically predicted excellent π‐acceptor character of HAsAsH, and is tantamount to full reduction to the diarsane‐1,2‐diide form.     

Redox and Coordination Behavior of the Hexaphosphabenzene Ligand in [(Cp*Mo)2(μ,η6:η6‐P6)] Towards the “Naked” Cations Cu+, Ag+, and Tl+

Although the cyclo‐P₆ complex [(Cp*Mo)₂(μ,η⁶:η⁶‐P₆)] ( 1 ) was reported 30 years ago, little is known about its chemistry. Herein, we report a high‐yielding synthesis of 1 , the complex 2 , which contains an unprecedented cyclo‐P₁₀ ligand, and the reactivity of 1 towards the “naked” cations Cu⁺, Ag⁺, and Tl⁺. Besides the formation of the single oxidation products 3 a,b which have a bisallylic distorted cyclo‐P₆ middle deck, the [M( 1 )₂]⁺ complexes are described which show distorted square‐planar (M=Cu( 4 a ), Ag( 4 b )) or distorted tetrahedral coordinated (M=Cu( 5 )) M⁺ cations. The choice of solvent enabled control over the reaction outcome for Cu⁺, as proved by powder XRD and supported by DFT calculations. The reaction with Tl⁺ affords a layered two‐dimensional coordination network in the solid state.     

Nuclear magnetic relaxation in water revisited

In this study, we revisited nuclear magnetic relaxation of (1)H in water at very low Larmor frequencies that has been studied intensively in earlier years. We make use of the recently developed superconducting quantum interference device based ultra-low field NMR technique, which enables much easier access to the longitudinal spin-lattice relaxation time T(1) and the transversal spin-spin relaxation time T(2) below several kHz than traditional field cycling methods. Our data reproduce and complement the earlier results, in that they corroborate the finding of an exchange process with a correlation time of about 0.34 ms at room temperature which can be attributed to the migration of hydronium and hydroxyl ions in neutral water via hydrogen bridges. The corresponding relaxation process is driven by the interaction of the protons with (17)O and contributes to the T(1) and the T(2) relaxation rate by about 0.12 s(-1). In addition, we found evidence of a very slow exchange process at about 100 Hz that has hitherto not been reported.     

Germanium/phosphorus cage compounds with germanium in three different oxidation states

Novel germanium/phosphorus cage compounds with new structural motifs have been synthesized containing germanium in three different oxidation states. The key to obtain this new class of compounds is the use of monolithiated primary phosphine LiHPtBu in the reaction with GeX(2).     

High fidelity neuronal networks formed by plasma masking with a bilayer membrane: analysis of neurodegenerative and neuroprotective processes

Spatially defined neuronal networks have great potential to be used in a wide spectrum of neurobiology assays. We present an original technique for the precise and reproducible formation of neuronal networks. A PDMS membrane comprising through-holes aligned with interconnecting microchannels was used during oxygen plasma etching to dry mask a protein rejecting poly(ethylene glycol) (PEG) adlayer. Patterns were faithfully replicated to produce an oxidized interconnected array pattern which supported protein adsorption. Differentiated human SH-SY5Y neuron-like cells adhered to the array nodes with the micron-scale interconnecting tracks guiding neurite outgrowth to produce neuronal connections and establish a network. A 2.0 μm track width was optimal for high-level network formation and node compliance. These spatially standardized neuronal networks were used to analyse the dynamics of acrylamide-induced neurite degeneration and the protective effects of co-treatment with calpeptin or brain derived neurotrophic factor (BDNF).