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.     

Development of interdigitated arrays coated with functional polyaniline/MWCNT for electrochemical biodetection: application for human papilloma virus

In this study, polyaniline-multiwalled carbon nanotube film (PANi-MWCNT) has been polymerized on interdigitated platinum electrode arrays (IDA), fabricated by MEMS technology for the detection of human papillomavirus (HPV) infection, using immobilized peptide aptamers as affinity capture reagent. Label-free, electrochemical detection of the specific immune reaction between antigen peptide aptamer HPV-16-L1 (with a molecular weight of 1825 Da), the most common genotype in cytological normal women worldwide, and its specific antibody of HPV-16 (which is much bigger with molecular weight of ca. 150 kDa) on multifunctional PANi-MWCNT based arrays was reported. The most significant advantage of this technique consists of reagentless and multiple detection of antigen-antibody complex formation on well conducting IDA interface of PANi-MWCNT, without intermediate steps or any labeling reagents, as normally required in the previous works.     

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.     

Droplet synthesis of well-defined block copolymers using solvent-resistant microfluidic device

Well-defined diblock copolymers were synthesized via an exothermic RAFT route by a droplet microfluidic process using a solvent-resistant and thermally stable fluoropolymer microreactor fabricated by a non-lithographic embedded template method. The resulting polymers were compared to products obtained from continuous flow capillary reactor and conventional bulk synthesis. The droplet based microreactor demonstrated superior molecular weight distribution control by synthesizing a higher molecular weight product with higher conversion and narrow polydispersity in a much shorter reaction time. The high quality of the as-synthesized block copolymer PMMA-b-PS led to a generation of micelles with a narrow size distribution that could be used as a template for well-ordered mesoporous silica with regular frameworks and high surface areas.     

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.