q-Generalizations of a family of harmonic number identities

AbstractPaule and Schneider (2003) [3], and Chu (Chu and Donno) (2005) [1] gave a family of wonderful harmonic number identities. Their generalized versions associated with q-harmonic numbers will be established by applying a derivative operator to Watson's q-Whipple transformation

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

Electrospun PA66/Graphene Fiber Films and Application on Flexible Triboelectric Nanogenerators

Triboelectric nanogenerators (TENGs) are considered to be the most promising energy supply equipment for wearable devices, due to their excellent portability and good mechanical properties. Nevertheless, low power generation efficiency, high fabrication difficulty, and poor wearability hinder their application in the wearable field. In this work, PA66/graphene fiber films with 0, 1 wt%, 1.5 wt%, 2 wt%, 2.5 wt% graphene and PVDF films were prepared by electrospinning. Meanwhile, TENGs were prepared with PA66/graphene fiber films, PVDF films and plain weave conductive cloth, which were used as the positive friction layer, negative friction layer and the flexible substrate, respectively. The results demonstrated that TENGs prepared by PA66/graphene fiber films with 2 wt% grapheme showed the best performance, and that the maximum open circuit voltage and short circuit current of TENGs could reach 180 V and 7.8 μA, respectively, and that the power density was 2.67 W/m2 when the external load was 113 MΩ. This is why the PA66/graphene film produced a more subtle secondary network with the addition of graphene, used as a charge capture site to increase its surface charge. Additionally, all the layered structures of TENGs were composed of breathable electrospun films and plain conductive cloth, with water vapor transmittance (WVT) of 9.6 Kgm−2d−1, reflecting excellent wearing comfort. The study showed that TENGs, based on all electrospinning, have great potential in the field of wearable energy supply devices