Among the techniques that are used for signal denoising, smoothing filters have received significant attention during the past. However, these methods are particularly suited for polynomial signal smoothing. Therefore, their performance is significantly decreased for signals that cannot be well modelled with a polynomial function. To overcome this limitation, in this paper, we propose a new approach to smoothing filter design, which is based on the DELAY DIFFERENTIAL EQUATION model. In this approach, we propose to substitute the derivative of the signal with a DDE model of the signal. As an example, a DELAY DIFFERENTIAL EQUATION of moving average (MA) model is used as penalty term in the optimization problem. The results indicate that a better solution can be found by appropriate balancing a trade-off between the MA model of the signal and the minimum mean square error. The proposed MA smoothing filter is analyzed in frequency domain. It is shown that the proposed MA smoothing filter displays good properties within its pass-band and stop-band bands for small values of window length. As an application, the proposed MA smoothing filter was used for electrocardiogram (ECG) signal denoising. We tested the method over data from the PhysioNet PTB database. The results show that the proposed MA smoothing filter outperforms the original smoothness priors or QV regularization.

This paper is devoted to obtaining some new sufficient conditions for the oscillation of all solutions of first order nonlinear DIFFERENTIAL EQUATIONs with several deviating arguments. Finally, an illustrative example related to our results is given.

During an epidemic, existing mass media plays a fundamental role in promoting effective, trustworthy and convenient information regarding disease symptoms and prevention measures against the infection. In this research paper, we aim to explore the impact of media awareness projected to a SEIV compartmental model incorporating newly modulated saturated incidence function and discrete-time DELAY during an epidemic. We considered the time lag in between the process while unaware susceptible individuals would be aware through the campaign media. Sensitivity analysis reveals the influence of the model parameters in the progression of the epidemic. Numerical simulations enable us to visualize the importance of media awareness to convey predictions regarding the mitigation and apparent eradication of the epidemic.

Here, we study the logistic DELAY DIFFERENTIAL EQUATION with two different DELAYs. First of all, we disscuse the local stability and Hopf bifurcation conditons. The method of steps is used to get a discretized analogue of the original system. Local stability and bifurcation analysis of the discretized system is investigated. Finally, we carry out some numerical simulations such as bifurcation diagram, Lyapunov exponent and phase portraits to verify the theoretical results and to illustrate complex dynamics of the considered system.

This study presents a numerical approach for solving temporal fractionalorder singularly perturbed parabolic convection-diffusion DIFFERENTIAL EQUATIONs with a DELAY using a uniformly convergent scheme. We use the asymptotic analysis of the problem to offer a priori bounds on the exact solution and its derivatives. To discretize the problem, we use the implicit Euler technique on a uniform mesh in time and the midpoint upwind finite difference approach on a piece-wise uniform mesh in space. The proposed technique has a nearly first-order uniform convergence order in both spatial and temporal dimensions. To validate the theoretical analysis of the scheme, two numerical test situations for various values of ε are explored.

Introduction: The theory and application of linear and nonlinear DELAY DIFFERENTIAL EQUATIONs is an important subject within physics and applied mathematics.There are several numerical approaches for solving linear and nonlinear DELAY DIFFERENTIAL EQUATIONs.Aim: In this paper, DIFFERENTIAL transform method (DTM) is applied to numerical solution of linear and nonlinear DELAY DIFFERENTIAL EQUATIONs.Materials and Methods: In this work, we presented simple proofs of the DIFFERENTIAL transform Theorems and then we applied them to solving linear and nonlinear DELAY DIFFERENTIAL EQUATIONs.Results: Numerical results compared to exact solutions are reported and it is shown that DTM is a reliable tool for the solution of DELAY DIFFERENTIAL EQUATIONs.Conclusion: The present method reduces the computational difficulties of the other traditional methods and all the calculations can be made simple manipulations. Several examples were tested by applying the DTM and the results have shown remarkable performance.

In this paper, Artificial Neural Networks are used to solve DELAY DIFFERENTIAL EQUATIONs. We have suggested an appropriate approximation function based on ANN and then by solving an optimization problem of error function, the neural network is trained. The advantage of this technique is that the proposed approximation functions, with a slight modification, can be used for most types of DELAY DIFFERENTIAL EQUATIONs, including DDE with constant DELAY, time-dependent DELAY and pantograph DELAY. To demonstrate the effectiveness of the method, various examples have been tested and the validity and efficiency of the method have been shown.