On functional equations for meromorphic functions and applications

Donovan’s conjecture states that there exist only finitely many Morita equivalence classes of p-blocks with a given defect. This conjecture was shown by Radha Kessar to be equivalent to two other conjectures, one of which is that the basic algebras of p-blocks with a given defect can all be defined over a single finite field. We shall show that this latter conjecture is equivalent to the seemingly stronger statement that all p-blocks with a given defect can be defined over a single finite field.     

On the Stability and Solution Sensitivity of a Consumer Problem

We present a continuous-time generalization of the seminal research and development model of d’Aspremont and Jacquemin (Am Econ Rev 78(5):1133–1137, 1988) to examine the trade-off between the benefits of allowing firms to cooperate in research and the corresponding increased potential for product market collusion. We show the existence of a solution to the optimal investment problem using a combination of results from viscosity theory and the theory of planar dynamical systems. In particular, we show that there is a critical level of marginal cost at which firms are indifferent between doing nothing and starting to develop the technology. We find that colluding firms develop further a wider range of initial technologies, pursue innovations more quickly, and are less likely to abandon a technology. Product market collusion could thus yield higher total surplus.     

Novel route to size-controlled Fe-MIL-88B-NH2 metal-organic framework nanocrystals

A new approach for the synthesis of uniform metal-organic framework (MOF) nanocrystals with controlled sizes and aspect ratios has been developed using simultaneously the non-ionic triblock co-polymer F127 and acetic acid as stabilizing and deprotonating agents, respectively. The alkylene oxide segments of the triblock co-polymer can coordinate with metal ions and stabilize MOF nuclei in the early stage of the formation of MOF nanocrystals. Acetic acid can control the deprotonation of carboxylic linkers during the synthesis and, thus, enables the control of the rate of nucleation, leading to the tailoring of the size and aspect ratio (length/width) of nanocrystals. Fe-MIL-88B-NH(2), as an iron-based MOF crystal, was selected as a typical example to illustrate our approach. The results reveal that this approach is used for not only the synthesis of uniform nanocrystals but also the control of the size and aspect ratio of the materials. The size and aspect ratio of nanocrystals increase with an increase in the concentration of acetic acid in the synthetic mixture. The non-ionic triblock co-polymer F127 and acetic acid can be easily removed from the Fe-MIL-88B-NH(2) nanocrystal products by washing with ethanol, and thus, their amine groups are available for practical applications. The approach is expected to synthesize various nanosized carboxylate-based MOF members, such as MIL-53, MIL-89, MIL-100, and MIL-101.     

A-type cranberry proanthocyanidins inhibit the RANKL-dependent differentiation and function of human osteoclasts

This study investigated the effect of A-type cranberry proanthocyanidins (AC-PACs) on osteoclast formation and bone resorption activity. The differentiation of human pre-osteoclastic cells was assessed by tartrate-resistant acid phosphatase (TRAP) staining, while the secretion of interleukin-8 (IL-8) and matrix metalloproteinases (MMPs) was measured by ELISA. Bone resorption activity was investigated by using a human bone plate coupled with an immunoassay that detected the release of collagen helical peptides. AC-PACs up to 100 μg/mL were atoxic for osteoclastic cells. TRAP staining evidenced a dose-dependent inhibition of osteoclastogenesis. More specifically, AC-PACs at 50 μg/mL caused a 95% inhibition of RANKL-dependent osteoclast differentiation. This concentration of AC-PACs also significantly increased the secretion of IL-8 (6-fold) and inhibited the secretion of both MMP-2 and MMP-9. Lastly, AC-PACs (10, 25, 50 and 100 μg/ml) affected bone degradation mediated by mature osteoclasts by significantly decreasing the release of collagen helical peptides. This study suggests that AC-PACs can interfere with osteoclastic cell maturation and physiology as well as prevent bone resorption. These compounds may be considered as therapeutic agents for the prevention and treatment of periodontitis.     

Highly enantioselective Mannich reactions with α-aryl silyl ketene acetals and imines

Mannich reactions with chiral silicon Lewis acid activated acylhydrazones and α-aryl silyl ketene acetals and α-aryl,α-alkyl silyl ketene imines proceed efficiently and with good to excellent levels of both diastereoselectivity and enantioselectivity. The reactions provide access to α-aryl,β-hydrazido esters and α-aryl,α-alkyl,β-hydrazido nitriles, which are valuable analogs of β-amino acids.     

A new synthesis of pyrrolidines by way of an enantioselective Mannich/diastereoselective hydroamination reaction sequence

A new two-step synthesis of highly substituted pyrrolidines has been developed. Chiral silane Lewis acid promoted enantioselective Mannich reactions of silyl ketene imines with acylhydrazones may be used to access bishomoallylic benzoic hydrazides that in turn may be cyclized to pyrrolidines by way of the thermal hydroamination reaction reported recently by Beauchemin. Importantly, excellent diastereoselectivity may be realized in the hydroamination reactions.     

Quantifying temperature and flow rate effects on the performance of a fixed-bed chromatographic reactor

Chromatographic reactors are based on coupling chemical reactions with chromatographic separation in fixed-beds. Temperature and flow rate are important parameters for the performance of such reactors. Temperature affects mainly adsorption, chemical equilibria, mass transfer and reaction kinetics, whereas flow rate influences residence time and dispersion. In order to evaluate the mentioned effects, the hydrolysis reactions of methyl formate (MF) and methyl acetate (MA) were chosen as case studies. These reactions were performed experimentally in a lab-scale fixed-bed chromatographic reactor packed with a strong acidic ion exchange resin. The chosen reactions can be considered to represent a relative fast (MF) and a relative slow (MA) reaction. The processes which take place inside the reactor were described and simulated using an isothermal equilibrium dispersive model. The essential model parameters were determined experimentally at different temperatures and flow rates. The performance of the chromatographic reactor was evaluated at several discrete constant temperature levels by quantifying product purity, productivity and yield. The work provides insight regarding the influence of temperature and flow rate on values of the model parameters and the performance criteria.     

Electronic structures, vibrational and thermochemical properties of neutral and charged niobium clusters Nb(n), n = 7-12

Geometric and electronic structures, vibrational properties, and relative stabilities of niobium clusters Nb(n), n = 7-12, are studied using both DFT (BPW91 and M06 functionals) and CCSD(T) calculations with the cc-pVnZ-PP basis set. In each cluster, various lower-lying states are very close in energy in such a way that the ground state cannot be unambiguously established by DFT computations. Nb clusters tend to prefer the lowest possible spin state as the ground state, except for Nb(12) ((3)A(g)). The optimal structure of the cluster at a certain size does not simply grow from that of the smaller one by adding an atom randomly. Instead, the Nb clusters prefer a close-packed growth behavior. Nb(10) has a spherically aromatic character, high chemical hardness and large HOMO-LUMO gap. Electron affinities, ionization energies, binding energy per atom, and the stepwise dissociation energies are evaluated. Energetic properties exhibit odd-even oscillations. Comparison with experimental values shows that both BPW91 and M06 functionals are reliable in predicting the EA and IE values, but the BPW91 is deficient in predicting the binding and dissociation energies. We re-examine in particular the experimental far IR spectra previously recorded using the IR-MPD and free electron laser spectrometric techniques and propose novel assignments for Nb(7) and Nb(9) systems. The IR spectra of the anions are also predicted.     

Local shrinkage and stress induced by thermo-oxidation in composite materials at high temperatures

The paper is concerned with the modelling, simulation and experimental characterisation of local shrinkage strains and stresses induced by thermo-oxidation phenomena in the IM7/977-2 carbon/epoxy composite material at elevated temperatures. The oxygen concentration and mechanical fields were established through a coupled model constructed from a unified multiphysical approach and the thermodynamics of irreversible processes. The model was implemented in the ABAQUS^® finite element commercial code. Simulations of thermo-oxidation-induced matrix shrinkage were run at a local scale, i.e., the scale of the elementary constituents of the composite, the fibre and the matrix. The experimental assessment was done at the same scale, and the local matrix shrinkage profiles were measured by confocal interferometric microscopy.A good agreement was found between the simulated and measured profiles, validating the unified model. The thermo-oxidation induced stress field was analysed to understand the influence of the environment on the onset of damage in composite materials at elevated temperature.