Restricted testing conditions for the multilinear maximal operator

Restricted testing conditions were considered recently. For the maximal operator, Hytönen, Li and Sawyer [8] first obtained parental testing condition. Later, they [9] showed that it suffices to restrict testing to doubling cubes. Chen and Lacey [3] gave a similar restricted testing condition. In our paper, we discuss a version of the latter in the multilinear setting.

     

Biodistribution study of free and microencapsulated 6‐methylcoumarin in Wistar rats by HPLC

A sensitive, specific and reproducible HPLC method has been developed and validated for the quantitative determination of 6‐methylcoumarin (6MC) in plasma and other tissues in Wistar rats. A C₁₈ column was used with UV detection at 321 nm and a gradient system consisting of methanol‐deionized water was used as mobile phase. The retention time for 6MC was 14.921 min and no interfering peaks were observed for any of the matrices. Linear relationships (r² > 0.997) were obtained between the peak height ratios and the corresponding biological sample concentrations over the range 0.4–12.8 µg/mL. Precision and accuracy were evaluated; the coefficient of variation and the relative error for all of the organs were <2 and 7%, respectively. The limit of quantitation was 0.20 µg/mL for the heart and 0.30 µg/mL for the other tissues evaluated. This HPLC method was successfully used in the determination of 6MC in the biodistribution study after administration of 200 mg/kg of both 6MC‐free and 6MC‐loaded polymeric microparticles. In this study, extensive 6MC was found, in both free and microencapsulated forms, in all the organs tested. The 6MC‐free showed a range of between 1.7 and 11.5 µg/g, while the microencapsulated 6MC showed concentrations of between 6.35 and 17.7 µg/g, suggesting that 6MC improved absorption rate. Copyright © 2014 John Wiley & Sons, Ltd.     

Experimental and Theoretical Studies on the Rearrangement of 2‐Oxoazepane α,α‐Amino Acids into 2′‐Oxopiperidine β2,3,3‐Amino Acids: An Example of Intramolecular Catalysis

Enantiopure β‐amino acids represent interesting scaffolds for peptidomimetics, foldamers and bioactive compounds. However, the synthesis of highly substituted analogues is still a major challenge. Herein, we describe the spontaneous rearrangement of 4‐carboxy‐2‐oxoazepane α,α‐amino acids to lead to 2′‐oxopiperidine‐containing β^2,3,3‐amino acids, upon basic or acid hydrolysis of the 2‐oxoazepane α,α‐amino acid ester. Under acidic conditions, a totally stereoselective synthetic route has been developed. The reordering process involved the spontaneous breakdown of an amide bond, which typically requires strong conditions, and the formation of a new bond leading to the six‐membered heterocycle. A quantum mechanical study was carried out to obtain insight into the remarkable ease of this rearrangement, which occurs at room temperature, either in solution or upon storage of the 4‐carboxylic acid substituted 2‐oxoazepane derivatives. This theoretical study suggests that the rearrangement process occurs through a concerted mechanism, in which the energy of the transition states can be lowered by the participation of a catalytic water molecule. Interestingly, it also suggested a role for the carboxylic acid at position 4 of the 2‐oxoazepane ring, which facilitates this rearrangement, participating directly in the intramolecular catalysis.     

Conversion of Methanol to Aromatic-Rich Gasoline over High-Efficiency Bifunctional Catalysts: Green Synthesis of GaZSM-5 Zeolites via Dry-Gel Conversion Strategy

Russian Journal of Applied Chemistry - Nanoscale ZSM-5 (AlZ5-D) and Ga-substituted ZSM-5 zeolites ((Al,Ga)Z5-D and GaZ5-D) were synthesized by a green dry-gel conversion strategy. For comparison,...     

Thermal,morphostructural and spectrometric characterization of an antibacterial kaolinite-based filter modified with silver for water treatment

Journal of Thermal Analysis and Calorimetry - The aim of this work is to synthesize and characterize a new structured silver–clay dried, calcined or sintered at different temperatures...     

Mechanistic Aspects of a Highly Active Dinuclear Zinc Catalyst for the Co‐polymerization of Epoxides and CO2

The dinuclear zinc complex reported by us is to date the most active zinc catalyst for the co‐polymerization of cyclohexene oxide (CHO) and carbon dioxide. However, co‐polymerization experiments with propylene oxide (PO) and CO₂ revealed surprisingly low conversions. Within this work, we focused on clarification of this behavior through experimental results and quantum chemical studies. The combination of both results indicated the formation of an energetically highly stable intermediate in the presence of propylene oxide and carbon dioxide. A similar species in the case of cyclohexene oxide/CO₂ co‐polymerization was not stable enough to deactivate the catalyst due to steric repulsion.