To achieve high-throughput ultrasensitive detection of mycotoxins in food, a functional DNA-guided transition-state CRISPR/Cas12a microfluidic biosensor (named FTMB) was successfully constructed. The signal transduction CRISPR/Cas12a strategy in FTMB has utilized DNA sequences with a specific recognition function and activators to form trigger switches. Meanwhile, the transition-state CRISPR/Cas12a system was constructed by adjusting the composition ratio of crRNA and activator to achieve a high response for low concentrations of target mycotoxins. On the other hand, the signal enhancement of FTMB has efficiently integrated the signal output of quantum dots (QDs) with the fluorescence enhancement effect of photonic crystals (PCs). The construction of universal QDs for the CRISPR/Cas12a system and PC films matching the photonic bandgap produced a significant signal enhancement by a factor of 45.6. Overall, FTMB exhibited a wide analytic range (10–5–101 ng·mL–1), low detection of limit (fg·mL–1), short detection period (∼40 min), high specificity, good precision (coefficients of variation <5%), and satisfactory practical sample analysis capacity (the consistency with HPLC at 88.76%–109.99%). It would provide a new and reliable solution for the rapid detection of multiple small molecules in the fields of clinical diagnosis and food safety.

In this paper, we introduce a new family of generalized Bernstein operators based on q integers, called -Bernstein operators, denoted by . We investigate a Kovovkin-type approximation theorem, and obtain the rate of convergence of to any continuous functions f. The main results are the identification of several shape-preserving properties of these operators, including their monotonicity- and convexity-preserving properties with respect to . We also obtain the monotonicity with n and q of .

In this note, we give an elaboration of a basic problem on convergence theorem of -analogue of Bernstein-type operators. By some classical analysis techniques, we derive an exact class of -integer satisfying with and under . Our results provide an erratum to corresponding results on -analogue of Bernstein-type operators that appeared in recent literature.

In this paper we present a survey of rates of pointwise approximation of modified Gamma operators G n for locally bounded functions and absolutely continuous functions by using some inequalities and results of probability theory with the method of Bojanic-Cheng. In the paper a kind of locally bounded functions is introduced with different growth conditions in the fields of both ends of interval (0, +∞), and it is found out that the operators have different properties compared to the Gamma operators discussed in [X.M. Zeng, Approximation properties of Gamma operators, J. Math. Anal. Appl. 311 (2005) 389-401]. And we obtain two main theorems. Theorem 1 gives an estimate for locally bounded functions which subsumes the approximation of functions of bounded variation as a special case. Theorem 2 gives an estimate for absolutely continuous functions which is best possible in the asymptotical sense.

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