This paper is concerned with a class of Nicholson's blowflies model involving nonlinear density-dependent mortality terms and multiple pairs of time-varying delays. By using differential inequality techniques and the fluctuation lemma, we establish a delay-independent criterion on the global asymptotic stability of the addressed model, which improves and complements some existing ones. The effectiveness of the obtained result is illustrated by some numerical simulations.

This paper investigates a periodic Nicholson's blowflies equation with multiple time-varying delays. By using differential inequality techniques and the fluctuation lemma, we establish a criterion to ensure the global exponential stability on the positive solutions of the addressed equation, which improves and complements some existing ones. The effectiveness of the obtained result is illustrated by some numerical simulations.

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A class of 4-band symmetric biorthogonal wavelet bases has been constructed, in which any wavelet system the high-pass filters can be determined by exchanging position and changing the sign of the two low-pass filters. Thus, the least restrictive conditions are needed for forming a wavelet so that the free degrees can be reversed for application requirement. Some concrete examples with high vanishing moments are also given, the properties of the transformation matrix are studied and the optimal model is constructed. These wavelets can process the boundary conveniently, and they lead to highly efficient computations in applications.

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