Oscillation theory of q-difference equation

In this research article, the authors present the oscillation theory of the q-difference equation K(t)y(qt)+k(t/q)y(t/q)= r(t)y(t) where r(t) = k(t)+k(t/q)-q(t) In particular we prove that this q-difference equation is oscillatory or non-oscillatory for different conditions.

Explicit values of the oscillation bounds for linear delay differential equations with monotone argument

The problem of finding the oscillation bounds for first-order linear delay differential equations has been in the focus of the oscillation theory for a long time. Although numerous estimates for the oscillation bounds are available in the literature, their explicit values were not known. In this paper, we give the oscillation bounds explicitly in terms of the real branches of the Lambert [Formula: see text] function.

A novel feature selection algorithm based on damping oscillation theory

Feature selection is an important task in big data analysis and information retrieval processing. It reduces the number of features by removing noise, extraneous data. In this paper, one feature subset selection algorithm based on damping oscillation theory and support vector machine classifier is proposed. This algorithm is called the Maximum Kendall coefficient Maximum Euclidean Distance Improved Gray Wolf Optimization algorithm (MKMDIGWO). In MKMDIGWO, first, a filter model based on Kendall coefficient and Euclidean distance is proposed, which is used to measure the correlation and redundancy of the candidate feature subset. Second, the wrapper model is an improved grey wolf optimization algorithm, in which its position update formula has been improved in order to achieve optimal results. Third, the filter model and the wrapper model are dynamically adjusted by the damping oscillation theory to achieve the effect of finding an optimal feature subset. Therefore, MKMDIGWO achieves both the efficiency of the filter model and the high precision of the wrapper model. Experimental results on five UCI public data sets and two microarray data sets have demonstrated the higher classification accuracy of the MKMDIGWO algorithm than that of other four state-of-the-art algorithms. The maximum ACC value of the MKMDIGWO algorithm is at least 0.5% higher than other algorithms on 10 data sets.

An Oscillation Test for Solutions of Second-Order Neutral Differential Equations of Mixed Type

It is easy to notice the great recent development in the oscillation theory of neutral differential equations. The primary aim of this work is to extend this development to neutral differential equations of mixed type (including both delay and advanced terms). In this work, we consider the second-order non-canonical neutral differential equations of mixed type and establish a new single-condition criterion for the oscillation of all solutions. By using a different approach and many techniques, we obtain improved oscillation criteria that are easy to apply on different models of equations.

Second-order impulsive differential systems with mixed and several delays

In this work, we present new necessary and sufficient conditions for the oscillation of a class of second-order neutral delay impulsive differential equations. Our oscillation results complement, simplify and improve recent results on oscillation theory of this type of nonlinear neutral impulsive differential equations that appear in the literature. An example is provided to illustrate the value of the main results.