• Journal of the Semiconductor & Display Technology
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• v.22 no.2
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• pp.56-63
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• 2023

This paper presents a method using finite element analysis and topology optimization to address the issue of overdesign in pressure-explosion proof enclosure doors for semiconductor manufacturing processes. The design conducted in this paper focuses on the pattern design of the enclosure door and its fixation components. The process consists of a solid-filled model, a topology optimization model, and a post-processing model. By applying environmental conditions to each model and comparing the maximum displacement, maximum equivalent stress, and weight values, it was confirmed that a reduction of about 13% in weight is achievable.

• Journal of the Korean Mathematical Society
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• v.32 no.1
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• pp.7-15
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• 1995

Multigrid method has been used widely to solve elliptic problems because of its applicability to many class of problems and fast convergence ([1], [3], [9], [10], [11], [12]). The estimate of convergence rate of multigrid is one of the main objectives of the multigrid analysis ([1], [2], [5], [6], [7], [8]). In many problems, the convergence rate depends on the regularity of the solutions([5], [6], [8]). In this paper, we present an improved estimate of reduction factor of multigrid iteration based on the proof in [6].

• Journal of the Korean Society for Precision Engineering
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• v.20 no.11
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• pp.100-107
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• 2003

This paper represents a disturbance compensation control for attenuating disturbance responses. In the consideration of the requirements on the model accuracy in the model based compensator designs, an experimental feed forward compensator design based on adaptive estimation by Filtered-x least mean square (FXLMS) algorithm is proposed. The convergence properties of the FXLMS algorithm are discussed and its conditions for the asymptotic convergence are derived theoretically. The effectiveness of the proposed method and the theoretical proof are verified by computer simulation.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.5
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• pp.608-615
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• 1998

In this paper a second-order iterative learning control algorithm with feedback is proposed for the trajectory-tracking control of nonlinear dynamic systems with unidentified parameters. In contrast to other known methods, the proposed teaming control scheme utilize more than one past error history contained in the trajectories generated at prior iterations, and a feedback term is added in the learning control scheme for the enhancement of convergence speed and robustness to disturbances or system parameter variations. The convergence proof of the proposed algorithm is given in detail, and the sufficient condition for the convergence of the algorithm is provided. We also discuss the convergence performance of the algorithm when the initial condition at the beginning of each iteration differs from the previous value of the initial condition. The effectiveness of the proposed algorithm is shown by computer simulation result. It is shown that, by adding a feedback term in teaming control algorithm, convergence speed, robustness to disturbances and robustness to unmatched initial conditions can be improved.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.89-98
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• 1999

We propose some new iterative methods for solving the generalized variational inequalities where the underlying operator T is monotone. These methods may be viewed as projection-type meth-ods. Convergence of these methods requires that the operator T is only monotone. The methods and the proof of the convergence are very simple. The results proved in this paper also represent a signif-icant improvement and refinement of the known results.

• Nuclear Engineering and Technology
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• v.56 no.5
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• pp.1942-1942
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• 2024

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.791-800
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• 1998

We present a proof that, among all complex numbers, Duffin-Schaeffer's choice in the Neumann series expansion of the inverse of a frame operator has the best possible convergence rate.

• Research in Mathematical Education
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• v.17 no.2
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• pp.133-152
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• 2013

In this research, we investigated students' understanding of the definitions of sequence of continuous functions and its uniform convergence. We selected three female and three male students out of the senior class of a university and conducted questionnaire surveys 4 times. We examined students' concept images of sequence of continuous functions and its uniform convergence and also how they approach to the right concept definitions for those through several progressive questions. Furthermore, we presented some suggestions for effective teaching-learning for the sequences of continuous functions.

• Structural Engineering and Mechanics
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• v.5 no.4
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• pp.471-490
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• 1997

In this paper, the classical Irons' patch tests which have been generally accepted for the convergence proof of a finite element are performed for Mindlin plate bending elements with a special emphasis on the nonconforming elements. The elements considered are 4-node and 8-node quadrilateral isoparametric elements which have been dominantly used for the analyses of plate bending problems. It was recognized from the patch tests that some nonconforming Mindlin plate elements pass all the cases of patch tests even though nonconforming elements do not preserve conformity. Then, the clues for the Mindlin plate element to pass the Irons' patch tests are investigated. Also, the convergent characteristics of some nonconforming Mindlin plate elements that do not pass the Irons' patch tests are examined by weak patch tests. The convergence tests are performed on the benchmark numerical problems for both nonconforming elements which pass the patch tests and which do not. Some conclusions on the relationship between the patch test and convergence of nonconforming Mindlin plate elements are drawn.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.763-771
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• 2009

T.H. Kim, H.K. Xu, [Convergence of the modified Mann's iteration method for asymptotically strict pseudo-contractions, Nonlinear Anal.(2007),doi:l0.l016/j.na.2007.02.029.] proved the strong convergence for asymptotically strict pseudo-contractions by the classical CQ iterative method. In this paper, we apply the monotone CQ iterative method to modify the classical CQ iterative method of T.H. Kim, H.K. Xu, and to obtain the strong convergence theorems for asymptotically strict pseudo-contractions. In the proved process of this paper, Cauchy sequences method is used, so we complete the proof without using the demi-closedness principle, Opial's condition or others about weak topological technologies. In addition, we use a ingenious technology to avoid defining that F(T) is bounded. On the other hand, we relax the restriction on the control sequence of iterative scheme.