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Acephate is an organophosphorus pesticide (OP) that is widely used to control insects in agricultural fields such as in vegetables and fruits. Toxic OPs can enter human and animal bodies and eventually lead to chronic or acute poisoning. However, traditional enzyme inhibition and colorimetric methods for OPs detection usually require complicated detection procedures and prolonged time and have low detection sensitivity. High-sensitivity monitoring of trace levels of acephate residues is of great significance to food safety and human health. Here, we developed a simple method for ultrasensitive quantitative detection of acephate based on the carbon quantum dot (CQD)-mediated fluorescence inner filter effect (IFE). In this method, the fluorescence from CQDs at 460 nm is quenched by 2,3-diaminophenazine (DAP) and the resulting fluorescence from DAP at 558 nm is through an IFE mechanism between CQDs and DAP, producing ratiometric responses. The ratiometric signal I 558 / I 460 was found to exhibit a linear relationship with the concentration of acephate. The detection limit of this method was 0.052 ppb, which is far lower than the standards for acephate from China and EU in food safety administration. The ratiometric fluorescence sensor was further validated by testing spiked samples of tap water and pear, indicating its great potential for sensitive detection of trace OPs in complex matrixes of real samples. 

We obtain partial improvement toward the pointwise convergence problem of Schrödinger solutions, in the general setting of fractal measure. In particular, we show that, for $$n\geqslant 3$$ , $$\lim _{t\rightarrow 0}e^{it\unicode[STIX]{x1D6E5}}f(x)$$ $=f(x)$ almost everywhere with respect to Lebesgue measure for all $$f\in H^{s}(\mathbb{R}^{n})$$ provided that $s>(n+1)/2(n+2)$ . The proof uses linear refined Strichartz estimates. We also prove a multilinear refined Strichartz using decoupling and multilinear Kakeya.