Oscillation Criteria for Solutions of Neutral Differential Equations of Impulses Effect with Positive and Negative Coefficients

In this paper, some necessary and sufficient conditions are obtained to ensure the oscillatory of all solutions of the first order impulsive neutral differential equations. Also, some results in the references have been improved and generalized. New lemmas are established to demonstrate the oscillation property. Special impulsive conditions associated with neutral differential equation are submitted. Some examples are given to illustrate the obtained results.

Sparse Representation Based on Tunable Q-Factor Wavelet Transform for Whale Click and Whistle Extraction

Whale sounds may mix several elements including whistle, click, and creak in the same vocalization, which may overlap in time and frequency, so it leads to conventional signal separation techniques challenging to be applied for the signal extraction. Unlike conventional signal separation techniques which are based on the frequency bands, such as WT and EMD, tunable-Q wavelet transform (TQWT) can separate the objected signal into particular components with different structures according to its oscillation property and eliminate in-band noise using the basis pursuit method. Considering the characteristics of oscillatory and transient impulse, we propose a novel signal separation method for whale whistle and click extraction. The proposed method is performed by the following two steps: first, TQWT is used to construct the dictionary for sparse representation. Secondly, the whale click and whistle construction are performed by designing the basis pursuit denoising (BPD) algorithm. The proposed method has been compared with one of the popular signal decomposition techniques, i.e., the EMD method. The experimental results show that the proposed method has a better performance of click and whistle signal separation in comparison with the EMD algorithm.

A sharp oscillation property involving the critical Sobolev exponent for a class of superlinear elliptic problems

This paper studies the asymptotic behaviour as α := u(0) ↑∞ of the first zero R(α) of the radially symmetric solution of the semilinear equationin ℝn, n ≥ 1, where h > 0 and β > 1. We establish that R(α) = O(α−(β−1)/2) if n = 1, 2 or n ≥ 3 and β < (n + 2)/(n − 2), and conjecture that lim inf α→∞R(α) > 0 if n ≥ 3 and β > (n + 2)/(n − 2).