• Journal of the Korean Mathematical Society
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• v.50 no.6
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• pp.1165-1181
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• 2013

In this paper, we consider a class of periodic It$\hat{o}$ stochastic delay differential equations by using the properties of periodic Markov processes, and some sufficient conditions for the existence of periodic solution of the delay equations are given. These existence theorems improve the results obtained by It$\hat{o}$ et al. [6], Bainov et al. [1] and Xu et al. [15]. As applications, we study the existence of periodic solution of periodic stochastic logistic equation and periodic stochastic neural networks with infinite delays, respectively. The theorem for the existence of periodic solution of periodic stochastic logistic equation improve the result obtained by Jiang et al. [7].

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.813-838
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• 2011

In this paper, we prove sufficient conditions for controllability of second order semi-linear neutral impulsive differential inclusions on unbounded domain with infinite delay in Banach spaces using the theory of strongly continuous Cosine families. We shall rely on a fixed point theorem due to Ma for multi-valued maps. The controllability results in infinite dimensional space has been proved without compactness on the family of Cosine operators.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.519-532
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• 2016

We consider the first initial boundary value problem for the 2D non-autonomous g-Navier-Stokes equations with infinite delays. We prove the existence of a pullback $\mathcal{D}$-attractor for the continuous process associated to the problem with respect to a large class of non-autonomous forcing terms.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.49-58
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• 2010

In the present article we consider the diffusive Nicholson's blowflies equation with nonlocal delay incorporated into an integral convolution over all the past time and the whole infinite spatial domain $\mathbb{R}$. When the kernel function takes a special function, we construct a pair of lower and upper solutions of the corresponding travelling wave equation and obtain the existence of travelling fronts according to the existence result of travelling wave front solutions for reaction diffusion systems with nonlocal delays developed by Wang, Li and Ruan (J. Differential Equations, 222(2006), 185-232).

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1549-1556
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• 2011

In this paper, we give an estimate on the difference between $x^n(t)$ and x(t) and it clearly shows that one can use the Picard iteration procedure to the approximate solutions to stochastic functional differential equations with infinite delay at phase space BC(($-{\infty}$, 0] : $R^d$) which denotes the family of bounded continuous $R^d$-valued functions ${\varphi}$ defined on ($-{\infty}$, 0] with norm ${\parallel}{\varphi}{\parallel}={\sup}_{-{\infty}<{\theta}{\leq}0}{\mid}{\varphi}({\theta}){\mid}$ under non-Lipschitz condition being considered as a special case and a weakened linear growth condition.

• Journal of Applied and Pure Mathematics
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• v.5 no.1_2
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• pp.23-40
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• 2023

This paper is concerned by the controllability results of impulsive neutral stochastic functional integrodifferential equations (INSFIDEs) driven by fractional Brownian motion with infinite delay in a real separable Hilbert space. The controllability results are obtained using stochastic analysis, Krasnoselkii fixed point method and the theory of resolvent operator in the sense of Grimmer. A practical example is provided to illustrate the viability of the abstract result of this work.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.3
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• pp.289-297
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• 2014

This article surveys the control theoretic study on time delay systems. Since time delay systems are infinite dimensional, there are not analytic but numerical solutions on almost analysis and synthesis problems, which implies that there are a tremendous number of approximated solutions. To show how to find such solutions, several results are summarized in terms of two different axes: 1) theoretic tools like integral inequality associated with the derivative of delay terms, Jensen inequality, lower bound lemma for reciprocal convexity, and Wirtinger-based inequality and 2) various candidates for Laypunov-Krasovskii functionals.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.33A no.11
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• pp.78-87
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• 1996

in urban cross-roads with dense buildings, receiving power and delay spread were computed when doing these, we were able to develope codes to be executed in a very fast time by combining image method and algorithm for propagation paths compairing with ray launching technique. And receiving power and delay spread could be viewed in 3-dimensional picture by virtue of computing electric fields in arbitrary receiving point. For numerical computation, receiving power of wide and anrrow band and delay spread were computed, and extension method of ray numbers was facilitated for handling infinite number of rays.

• Journal of Mechanical Science and Technology
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• v.18 no.7
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• pp.1131-1139
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• 2004

A new impedance controller is proposed for bilateral teleoperation under a time delay. The proposed controller does not need to measure or estimate the time delay in the communication channel using the force loop-back. In designing a stable impedance controller, absolute stability is used as a stability analysis tool, which results in a less conservative controller than the passivity concept. Moreover, in order to remove the conservatism associated with the assumption of infinite port impedances, the boundaries of human and environment impedance are set to finite values. Based on this, this paper proposes a parameter design procedure for stable impedance controllers. The validity of the proposed control scheme is demonstrated by experiments with a 1-dof master/slave system.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.4
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• pp.1683-1689
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• 2013

Applying Markov Stochastic Process theory, this paper attempts to suggest a tentative model explaining how private information may cause bargaining delay. It is shown that the bargaining delay is critically dependent on the specification of information. It turns out that the delay tends to be longer in bargaining where information is imperfect. This means that bargaining models frequently can have an infinite delay under imperfect information while they have finite delay of bargaining before reaching the agreements if information is perfect. Other interesting result is that bargaining delay may depend on who makes the offer first. And it is also shown that bargaining tends to end earlier if both players (seller and buyer) can make offers in turn than the case where only one side make a offer.