• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.39-53
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• 2014

In this paper, a non-asymptotic method is presented for solving singularly perturbed delay differential equations whose solution exhibits a boundary layer behavior. The second order singularly perturbed delay differential equation is replaced by an asymptotically equivalent first order neutral type delay differential equation. Then, Simpson's integration formula and linear interpolation are employed to get three term recurrence relation which is solved easily by Discrete Invariant Imbedding Algorithm. Some numerical examples are given to validate the computational efficiency of the proposed numerical scheme for various values of the delay and perturbation parameters.

• Journal of Applied and Pure Mathematics
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• v.4 no.3_4
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• pp.151-184
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• 2022

In the article, we handle with the existence and controllability results for fractional impulsive neutral functional integro-differential equation in Banach spaces. We have used advanced phase space definition for infinite delay. State dependent infinite delay is the main motivation using advanced version of phase space. The results are acquired using Schaefer's fixed point theorem. Examples are given to illustrate the theory.

• Structural Engineering and Mechanics
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• v.58 no.6
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• pp.1127-1143
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• 2016

The pounding phenomenon in adjacent structures happens in severing earthquakes that can cause great damages. Connecting neighboring structures with active and semi-active control devices is an effective method to avoid mutual colliding between neighboring buildings. One of the most important issues in control systems is applying online control force. There will be a time delay if the prose of producing control force does not perform on time. This paper proposed a time-delay compensation method in coupled structures control, with semi-active Magnetorheological (MR) damper. This method based on Newmark's integration is adopted to mitigate the time-delay effect. In this study, Lyapunov's direct approach is employed to compute demanded voltage for MR dampers. Using Lyapunov's direct algorithm guarantees the system stability to design a controller based on feedback. Because of the strong nonlinearity of MR dampers, the equation of motion of coupled structures becomes an involved equation, and it is impossible to solve it with the common time step methods. In present paper modified Newmark-Beta integration based on the instantaneous optimal control algorithm, used to solve the involved equation. In this method, the response of a coupled system estimated base on optimal control force. Two MDOF structures with different degrees of freedom are finally considered as a numeric example. The numerical results show, the Newmark compensation is an efficient method to decrease the negative effect of time delay in coupled systems; furthermore, instantaneous optimal control algorithm can estimate the response of structures suitable.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.449-455
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• 2007

We obtain a discrete version of a fundamental result by Yoshizawa related to the existence of almost periodic solutions of functional differential equations with finite delay.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.321-338
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• 2020

In this paper, we investigate the viscoelastic plate equation with a constant delay term and logarithmic nonlinearities. Under some conditions, we will prove the global existence. Furthermore, we use weighted spaces to establish a general decay rate of solution.

• Honam Mathematical Journal
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• v.26 no.4
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• pp.441-453
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• 2004

In this paper, sufficient conditions for the controllability of integrodifferential systems are established. The results are obtained by using the Schauder fixed point theorem and the resolvent operator. Example is provided to illustrate the theory.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.561-568
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• 2011

We investigate the stability property and existence of almost periodic solutions of discrete Volterra equations with unbounded delay.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.753-762
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• 2012

We study the BS-stability and the $\rho$-stability for functional difference equations with infinite delay as a discretization of Murakami and Yoshizawa's results [6] for functional differential equation with infinite delay.

• East Asian mathematical journal
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• v.19 no.1
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• pp.91-102
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• 2003

In this paper we prove the existence of mild and strong solutions of nonlinear delay integrodifferential equations with nonlocal conditions. The results are obtained by using the Schauder fixed point theorem and resolvent operator.

• Structural Engineering and Mechanics
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• v.20 no.2
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• pp.191-207
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• 2005

Time delay exists inevitably in active control, which may not only degrade the system performance but also render instability to the dynamic system. In this paper, a novel active controller is developed to solve the time delay problem in flexible structures. By using the independent modal space control method, the differential equation of the controlled mode with time delay is obtained from the time-delay system dynamics. Then it is discretized and changed into a first-order difference equation without any explicit time delay by augmenting the state variables. The modal controller is derived based on the augmented system using the discrete variable structure control method. The switching surface is determined by minimizing a discrete quadratic performance index. The modal coordinate is extracted from sensor measurements and the actuator control force is converted from the modal one. Since the time delay is explicitly included throughout the entire controller design without any approximation, the system performance and stability are guaranteed. Numerical simulations show that the proposed controller is feasible and effective in active vibration control of dynamic systems with time delay. If the time delay is not explicitly included in the controller design, instability may occur.