Harmonic Functions on Rank One Asymptotically Harmonic Manifolds

Asymptotically harmonic manifolds are simply connected complete Riemannian manifolds without conjugate points such that all horospheres have the same constant mean curvature \(h\). In this article we present results for harmonic functions on rank one asymptotically harmonic manifolds \(X\) with mild curvature boundedness conditions. Our main results are (a) the explicit calculation of the Radon–Nikodym derivative of the visibility measures, (b) an explicit integral representation for the solution of the Dirichlet problem at infinity in terms of these visibility measures, and (c) a result on horospherical means of bounded eigenfunctions implying that these eigenfunctions do not admit non-trivial continuous extensions to the geometric compactification \(\overline{X}\).     

Mechanochemical Synthesis of 3d Transition‐Metal–1,2,4‐Triazole Complexes as Precursors for Microwave‐Assisted and Thermal Conversion to Coordination Polymers with a High Influence on the Dielectric Properties

The complexes [MCl₂(TzH)₄] (M=Mn ( 1 ), Fe ( 2 ); TzH=1,2,4‐1H‐triazole) and [ZnCl₂(TzH)₂] ( 3 ) have been obtained by mechanochemical reactions of the corresponding divalent metal chloride and 1,2,4‐1H‐triazole. They were successfully used as precursors for the formation of coordination polymers either by a microwave‐assisted reaction or by thermal conversion. For manganese, the conversion directly yielded [MnCl₂TzH] ( 4 ), whereas for the iron‐containing precursor, [FeCl₂TzH] ( 6 ), was formed via the intermediate coordination polymer [FeCl(TzH)₂]Cl ( 5 ). For cobalt, the isotypic polymer [CoCl(TzH)₂]Cl ( 7 ) was obtained, but exclusively by a microwave‐induced reaction directly from CoCl₂. The crystal structures were resolved from single crystals and powders. The dielectric properties were determined and revealed large differences in permittivity between the precursor complexes and the rigid chain‐like coordination polymers. Whereas the monomeric complexes exhibit very different dielectric behaviour, depending on the transition metal, from “low‐k” to “high‐k” with the permittivity ranging from 4.3 to >100 for frequencies of up to 1000 Hz, the coordination polymers and complexes with strong intermolecular interactions are all close to “low‐k” materials with very low dielectric constants up to 50 °C. Therefore, the conversion procedures can be used to deliberately influence the dielectric properties from complex to polymer and for different 3d transition‐metal ions.     

Recent advances in capillary electrophoretic migration techniques for pharmaceutical analysis (2013–2015)

This review updates and follows‐up a previous review by highlighting recent advancements regarding capillary electromigration methodologies and applications in pharmaceutical analysis. General approaches such as quality by design as well as sample injection methods and detection sensitivity are discussed. The separation and analysis of drug‐related substances, chiral CE, and chiral CE‐MS in addition to the determination of physicochemical constants are addressed. The advantages of applying affinity capillary electrophoresis in studying receptor–ligand interactions are highlighted. Finally, current aspects related to the analysis of biopharmaceuticals are reviewed. The present review covers the literature between January 2013 and December 2015.     

On a question of Külshammer for representations of finite groups in reductive groups

Let G be a simple algebraic group of type G₂ over an algebraically closed field of characteristic 2. We give an example of a finite group Γ with Sylow 2-subgroup Γ₂ and an infinite family of pairwise non-conjugate homomorphisms ρ: Γ → G whose restrictions to Γ₂ are all conjugate. This answers a question of Burkhard Külshammer from 1995. We also give an action of Γ on a connected unipotent group V such that the map of 1-cohomologies H¹(Γ, V) → H¹(Γ_p, V) induced by restriction of 1-cocycles has an infinite fibre.     

Fast and efficient in silico 3D screening: toward maximum computational efficiency of pharmacophore-based and shape-based approaches

In continuation of our recent studies on the quality of conformational models generated with CATALYST and OMEGA we present a large-scale survey focusing on the impact of conformational model quality and several screening parameters on pharmacophore-based and shape-based virtual high throughput screening (vHTS). Therefore, we collected known active compounds of CDK2, p38 MAPK, PPAR-gamma, and factor Xa and built a set of druglike decoys using ilib:diverse. Subsequently, we generated 3D structures using CORINA and also calculated conformational models for all compounds using CAESAR, CATALYST FAST, and OMEGA. A widespread set of 103 structure-based pharmacophore models was developed with LigandScout for virtual screening with CATALYST. The performance of both database search modes (FAST and BEST flexible database search) as well as the fit value calculation procedures (FAST and BEST fit) available in CATALYST were analyzed in terms of their ability to discriminate between active and inactive compounds and in terms of efficiency. Moreover, these results are put in direct comparison to the performance of the shape-based virtual screening platform ROCS. Our results prove that high enrichment rates are not necessarily in conflict with efficient vHTS settings: In most of the experiments, we obtained the highest yield of actives in the hit list when parameter sets for the fastest search algorithm were used.     

Microscopic Li self-diffusion parameters in the lithiated anode material Li4 + xTi5O12 (0 < or = x < or = 3) measured by 7Li solid state NMR

The microscopic Li diffusion parameters in the lithiated spinel Li4 + xTi5O12, which is on its way to become a commercially used anode material in Li ion batteries, are probed for the first time via nuclear magnetic resonance spectroscopy.     

Lactonisation--a degradation pathway for active pharmaceutical compounds: an in silico study in amorphous trehalose

The lactonisation of a CCR1 inhibitor (CC chemokine receptor 1, involved in autoimmune diseases) featuring a hydroxyl group in a gamma-position (gamma-OH) with respect to an amide group has been investigated in silico. The two key steps of the lactonisation reaction are (i) rearrangement to an optimal conformation and (ii) the formation of the lactone (ring closure) and expulsion of NH3. Quantum chemical calculations in the gas phase were employed to identify conformers of the molecule with favorable starting geometries for a lactonisation reaction. In total, calculations of 1296 conformers revealed that it is energetically feasible for an inhibitor molecule to adopt a conformation where the carbon atom of the amide group (C(amide)) is suitably close to the oxygen atom of the gamma-OH (O(gamma)) to facilitate a successful lactonisation reaction. Additionally, molecular dynamics methods were used to show that rearrangement to a suitable conformer for lactonisation to occur happens to a lesser extent when the CCR1 inhibitor was embedded in an amorphous trehalose matrix (a model carbohydrate excipient). The mechanism of the actual lactonisation was investigated using the complete Linear Synchronous Transit/Quadratic Synchronous Transit (LST/QST) method. This was performed in both the gas phase and in water and was found to be a concerted reaction.     

How realistic is the pore size distribution calculated from adsorption isotherms if activated carbon is composed of fullerene-like fragments?

A plausible model for the structure of non-graphitizing carbon is one which consists of curved, fullerene-like fragments grouped together in a random arrangement. Although this model was proposed several years ago, there have been no attempts to calculate the properties of such a structure. Here, we determine the density, pore size distribution and adsorption properties of a model porous carbon constructed from fullerene-like elements. Using the method proposed recently by Bhattacharya and Gubbins (BG), which was tested in this study for ideal and defective carbon slits, the pore size distributions (PSDs) of the initial model and two related carbon models are calculated. The obtained PSD curves show that two structures are micro-mesoporous (with different ratio of micro/mesopores) and the third is strictly microporous. Using the grand canonical Monte Carlo (GCMC) method, adsorption isotherms of Ar (87 K) are simulated for all the structures. Finally PSD curves are calculated using the Horvath-Kawazoe, non-local density functional theory (NLDFT), Nguyen and Do, and Barrett-Joyner-Halenda (BJH) approaches, and compared with those predicted by the BG method. This is the first study in which different methods of calculation of PSDs for carbons from adsorption data can be really verified, since absolute (i.e. true) PSDs are obtained using the BG method. This is also the first study reporting the results of computer simulations of adsorption on fullerene-like carbon models.