Let a, b and n be positive integers with a > b. In this note, we prove that (2bn + 1)(2bn + 3) ( 2bn bn )∣∣∣∣3(a− b)(3a− b)(2an an )( an bn ) . This confirms a recent conjecture of Amdeberhan and Moll.

Following Sun and Moll [4], we study vp(T (N)), the p-adic valuation of the counting function of the alternating sign matrices. We find an exact analytic expression for it that exhibits the fluctuating behaviour, by means of Fourier coefficients. The method is the Mellin-Perron technique, which is familiar in the analysis of the sum-of-digits function and related quantities.

Machine Learning (ML) and Artificial Intelligence (AI) depend on data sources to train, improve, make predictions through their algorithms. With the digital revolution current paradigms like Internet of Things, this information is turning from static continuous streams. However, most ML/AI frameworks used nowadays are not fully prepared for revolution. In paper, we propose Kafka-ML, a novel ope...

Testing of rapidly growing species of mycobacteria (RGM) against antibacterial agents has been shown to have some clinical utility. This work establishes the MICs of seven antimicrobial agents following the guidelines set forth by the Clinical and Laboratory Standards Institute (CLSI) against eighteen isolates of Mycobacterium massiliense recovered from wound samples of patients submitted to mi...

BACKGROUND Patient satisfaction questionnaires are increasingly used for assessing quality of care. AIM To review the evidence for the reliability and validity of patient satisfaction questionnaires for out-of-hours care. DESIGN Systematic review. SETTING Primary care out-of-hours services. METHOD Searches of CINAHL, EMBASE, MEDLINE((R)) and PsycINFO using terms relevant to the measurem...

Magnetic nanoparticles based on Fe3O4 were prepared by a facile and rapid one-pot solvothermal synthesis using FeCl3·6H2O as a source of iron ions, ethylene glycol as a solvent and NH4Ac, (NH4)2CO3, NH4HCO3 or aqueous NH3 as precipitating and nucleating agents. In contrast to previous reports we reduce the synthesis time to 30 minutes using a pressurized microwave reactor without the requiremen...

The five-coordinate compound, Salen((t)Bu)Al(Ac), prepared in situ from Salen((t)Bu)AlBr and NH4Ac, forms Lewis acid-base adducts in aqueous solution with the G-type nerve agents, Sarin and Soman, and the VX hydrolysis product, ethylmethylphosphonate (EMPA). The resulting compounds, [Salen((t)Bu)Al(NA)](+)[Ac] (-) (with NA = Sarin, Soman, and EMPA) are sufficiently stable to be identified by ES...