• The Transactions of The Korean Institute of Electrical Engineers
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• v.63 no.4
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• pp.519-525
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• 2014

In this paper, an alternative variable structure controller is designed for the point-to-point regulation control of uncertain general linear plants so that the output of plants can be controlled from an arbitrarily given initial point to an arbitrarily given reference point in the state space. By using the error between the steady state value of the output and an arbitrarily given reference point and those integral, a transformed integral sliding surface is defined, in advance, as the surface from an initial state to an arbitrarily given reference point without the reaching phase problems. A corresponding control input is suggested to satisfy the existence condition of the sliding mode on the preselected transformed integral sliding surface against matched uncertainties and disturbances. Therefore, the output controlled by the proposed controller is completely robust and identical to that of the preselected transformed integral sliding surface. Through an example, the effectiveness of the suggested controller is verified.

• Journal of the Korean Mathematical Society
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• v.52 no.1
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• pp.125-139
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• 2015

In this paper we introduce the notion of the generalized Darbo fixed point theorem and prove some fixed and coupled fixed point theorems in Banach space via the measure of non-compactness, which generalize the result of Aghajani et al. [6]. Our results generalize, extend, and unify several well-known comparable results in the literature. One of the applications of our main result is to prove the existence of solutions for the system of integral equations.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.1-14
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• 2018

In this paper, we prove the existence, uniqueness and stability of solution for some nonlinear functional-integral equations by using generalized coupled Lipschitz condition. We prove a fixed point theorem to obtain the mentioned aim in Banach space $X=C([a,b],{\mathbb{R}})$. As application we study some volterra integral equations with linear, nonlinear and single kernel.

• Structural Engineering and Mechanics
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• v.34 no.1
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• pp.85-95
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• 2010

In this paper, numerical solution of the singular integral equation for the multiple curved branch-cracks is investigated. If some quadrature rule is used, one difficult point in the problem is to balance the number of unknowns and equations in the solution. This difficult point was overcome by taking the following steps: (a) to place a point dislocation at the intersecting point of branches, (b) to use the curve length method to covert the integral on the curve to an integral on the real axis, (c) to use the semi-open quadrature rule in the integration. After taking these steps, the number of the unknowns is equal to the number of the resulting algebraic equations. This is a particular advantage of the suggested method. In addition, accurate results for the stress intensity factors (SIFs) at crack tips have been found in a numerical example. Finally, several numerical examples are given to illustrate the efficiency of the method presented.

• East Asian mathematical journal
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• v.17 no.1
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• pp.33-45
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• 2001

In this paper an improved version of a fixed point theorem of the present author [3] in Banach algebras is obtained under the weaker conditions with a different method and using measure of non-compactness. The newly developed fixed point theorem is further-applied to certain nonlinear integral equations of mixed type for proving the existence theorems and stability of the solution in Banach algebras.

• The Pure and Applied Mathematics
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• v.30 no.3
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• pp.249-267
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• 2023

This manuscript is divided into three segments. In the first segment, we prove a unique common fixed point theorem satisfying generalized weak contraction on partially ordered metric spaces and also give an example to support our results presented here. In the second segment of the article, some common coupled fixed point results are derived from our main results. In the last segment, we investigate the solution of integral equation as an application. Our results generalize, extend and improve several well-known results of the existing literature.

• The Pure and Applied Mathematics
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• v.30 no.4
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• pp.443-461
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• 2023

In this paper, we establish some common fixed point theorems satisfying contraction mapping principle on partially ordered non-Archimedean fuzzy metric spaces and also derive some coupled fixed point results with the help of established results. We investigate the solution of integral equation and also give an example to show the applicability of our results. These results generalize, improve and fuzzify several well-known results in the recent literature.

• Nuclear Engineering and Technology
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• v.53 no.8
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• pp.2556-2563
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• 2021

Metaheuristic algorithms can work well in solving or optimizing problems, especially those that require approximation or do not have a good analytical solution. Particle swarm optimization (PSO) is one of these algorithms. The response quality of these algorithms depends on the objective function and its regulated parameters. The nonlinear nature of the pressurized light-water nuclear reactor (PWR) dynamics is a significant target for PSO. The two-point kinetics model of this type of reactor is used because of fission products properties. The proportional-integral-derivative (PID) controller is intended to control the power level of the PWR at a short-time transient. The absolute error (IAE), integral of square error (ISE), integral of time-absolute error (ITAE), and integral of time-square error (ITSE) objective functions have been used as performance indexes to tune the PID gains with PSO. The optimization results with each of them are evaluated with the number of function evaluations (NFE). All performance indexes achieve good results with differences in the rate of over/under-shoot or convergence rate of the cost function, in the desired time domain.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.523-536
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• 2007

Sharp error estimates in approximating the Stieltjes integral with bounded integrands and bounded integrators respectively, are given. Applications for three point quadrature rules of n-time differentiable functions are also provided.

• East Asian mathematical journal
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• v.34 no.5
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• pp.651-660
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• 2018

This paper concerned the existence of positive solutions to the second order differential systems with strongly coupled integral boundary value conditions. By using Krasnoselskii fixed point theorem, we prove the existence of positive solutions according to the parameters under the proper nonlinear growth conditions.