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APPROXIMATION PROPERTIES OF PAIRS OF SUBSPACES

  • Lee, Keun Young
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.3
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    • pp.563-568
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    • 2019
  • This study is concerned with the approximation properties of pairs. For ${\lambda}{\geq}1$, we prove that given a Banach space X and a closed subspace $Z_0$, if the pair ($X,Z_0$) has the ${\lambda}$-bounded approximation property (${\lambda}$-BAP), then for every ideal Z containing $Z_0$, the pair ($Z,Z_0$) has the ${\lambda}$-BAP; further, if Z is a closed subspace of X and the pair (X, Z) has the ${\lambda}$-BAP, then for every separable subspace $Y_0$ of X, there exists a separable closed subspace Y containing $Y_0$ such that the pair ($Y,Y{\cap}Z$) has the ${\lambda}$-BAP. We also prove that if Z is a separable closed subspace of X, then the pair (X, Z) has the ${\lambda}$-BAP if and only if for every separable subspace $Y_0$ of X, there exists a separable closed subspace Y containing $Y_0{\cup}Z$ such that the pair (Y, Z) has the ${\lambda}$-BAP.

System simulation and synchronization for optimal evolutionary design of nonlinear controlled systems

  • Chen, C.Y.J.;Kuo, D.;Hsieh, Chia-Yen;Chen, Tim
    • Smart Structures and Systems
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    • v.26 no.6
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    • pp.797-807
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    • 2020
  • Due to the influence of nonlinearity and time-variation, it is difficult to establish an accurate model of concrete frame structures that adopt active controllers. Fuzzy theory is a relatively appropriate method but susceptible to human subjective experience to decrease the performance. This paper proposes a novel artificial intelligence based EBA (Evolved Bat Algorithm) controller with machine learning matched membership functions in the complex nonlinear system. The proposed affine transformed membership functions are adopted and stabilization and performance criterion of the closed-loop fuzzy systems are obtained through a new parametrized linear matrix inequality which is rearranged by machine learning affine matched membership functions. The trajectory of the closed-loop dithered system and that of the closed-loop fuzzy relaxed system can be made as close as desired. This enables us to get a rigorous prediction of stability of the closed-loop dithered system by establishing that of the closed-loop fuzzy relaxed system.

Relation Between the Repulsive Interaction and the Overlap of the Electron Densities$^\dag$

  • Heo, Hoon;Shin, Kook-Joe;Kim, Yung-Sik
    • Bulletin of the Korean Chemical Society
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    • v.10 no.3
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    • pp.238-242
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    • 1989
  • The relations between the repulsive interactions and the electron density overlaps are investigated for various closed shell-closed shell pairs, including the systems containing alkali and halide ions. It is found that the repulsive interaction($V_{rep}$) depends on the overlap of the electron density($S_{\rho}$) according to a simple exponential relation, $V_{rep}$ = $As_{\rho}\;^{\alpha}$. Furthermore, for most of the closed shell systems the $\alpha$ values are near unity and the A values do not vary much. The same tests are also performed for the open shell-closed shell, and the open shell-open shell pairs. Although the results for these systems also show exponential dependences of the repulsive interactions on the density overlaps, the details of the dependence differ greatly from those for the closed shell systems and also vary widely from one individual system to another.

Numerical Study on the Effect of Exhaust Flow Pattern under Real Running Condition on the Performance and Reliability of Closed-Coupled Catalyst (실 운전조건에서의 배기유동패턴이 근접장착 촉매변환기의 성능 및 신뢰성에 미치는 영향에 관한 수치적 연구)

  • 정수진;김우승
    • Transactions of the Korean Society of Automotive Engineers
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    • v.12 no.2
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    • pp.54-61
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    • 2004
  • The engine-out flow is highly transient and hot, and may place tremendous thermal and inertial loads on a closed-coupled catalyst. Therefore, time-dependent and detailed flow and thermal field simulation may be crucial. The aim of this study is to develop combined chemical reaction and multi-dimensional fluid dynamic mathematical model and to study the effect of unsteady pulsating thermal and flow characteristics on thermal reliability of closed-coupled catalyst. The effect of cell density on the conversion performance under real running condition is also investigated. Unlike previous studies, the present study focuses on coupling between the problems of pulsating flow pattern and catalyst thermal response and conversion efficiency. The results are expressed in terms of temporal evolution of flow, pollutant and temperature distribution as well as transient characteristics of conversion efficiency. Fundamental understanding of the flow and thermal phenomena of closed-coupled catalyst under real running condition is presented. It is shown that instants of significantly low values of flow uniformity and conversion efficiency exist during exhaust blowdown and the temporal varaition of flow uniformity is very similar in pattern to one of conversion efficiency. It is also found that the location of hot spot in monolith is directly affected by transient flow pattern in closed-coupled catalyst.

A Study on the Planning Type of Elderly Welfare Facilities by Remodeling Closed School (폐교활용 노인요양시설의 유형별 공간계획에 관한 연구)

  • Kim, Jae-Young;Lee, Jong-Kuk
    • Journal of the Korean housing association
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    • v.24 no.2
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    • pp.69-76
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    • 2013
  • With people leaving the countryside to the cities as a result of industrialization and urbanization and drastic reduction of school children due to low birthrate, nationwide, total 3,438 schools have been shut down following the closed schools policy. Consequently, local governments have been active in selling, utilizing, and leasing the closed schools but there are still 466 closed schools that need to be addressed quickly. In addition to this phenomenon, aging population has become an important issue, and demand for elderly welfare facilities population is also increasing as a result. However, the supply of welfare services remains inadequate. This study was conducted in an attempt to solve both local and social problems at the same time, caused by the closing of schools and an aging population, through the use of closed schools as elderly welfare facilities, and suggests plans for per-unit space according to its type, and prototype, through research analysis of practical use, based on case studies. With the conclusions of both advantages and disadvantages, drawn from its type, we are hoping to be able to use this study by adapting its type, or mixing, according to one's needs.

Characteristics of Beeswax-treated Hanji Aged by Closed and Ventilated Chamber (밀폐 및 배기조건에서 열화된 밀랍지의 열화특성 분석)

  • Kang, Yeong Seok;Yang, Eun Jeong
    • Journal of Korea Technical Association of The Pulp and Paper Industry
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    • v.44 no.6
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    • pp.9-14
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    • 2012
  • Currently a variety of efforts to conserve and restore the injured the Annal of the Joseon Dynasty are continued and many studies about the aging pathway of the beeswax-treated volume have being progressed. In this study, two chambers were set up to assess the influence of VOCs(Volatile Organic Compounds) generated in process of beeswax deterioration. One chamber was closed and the other was continuously ventilated in order to remove the VOCs. In results, the acid compounds of beeswax-treated Hanjis aged in closed chamber was more than that aged in ventilated chamber. The folding endurance of beeswax-treated Hanjis aged in closed chamber was lower than that aged in ventilated chamber. Accumulated acid compounds of beeswax-treated Hanji in closed chamber may cause accelerated aging and strength decrease. In conclusion, accumulated acid compounds can accelerate the aging of beeswax-treated Hanji and cause the severe deterioration of inside of beeswax-treated volume. Therefore, to preserve more safely beeswax-treated volumes of the Annals of the Joseon Dynasty, it is essential that VOCs emitted from beeswax-treated volume are ventilated.

The Function Discovery of Closed Curve using a Bug Type of Artificial Life

  • Adachi, Shintaro;Yamashita, Kazuki;Serikawa, Seiichi;Shimomura, Teruo
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2003.09a
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    • pp.90-93
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    • 2003
  • The function, which represents the closed curve, is found from the sampling data by S-System in this study. Two methods are proposed. One is the extension of S-System. The data x and y are regarded as input data, and the data z=0 as output data. To avoid the trap into the invalid function, the judgment points (x$\_$j/, y/sug j/) are introduced. They are arranged in the inside and the outside of the closed curve. By introducing this concept, the functions representing closed curve are found by S-System. This method is simple because of a little extension of S-System. It is, however, difficult for the method to find the complex function like a hand-written curve. Then another method is also proposed. It uses the system incorporating the argument function. The closed curve can be expressed by the argument function. The relatively complex function, which represents the closed curve like a hand-written curve, is found by utilizing argument function.

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Stream Water Quality Monitoring in closed Valley Areas for Preserving Stream Water Quality of Puk'ansan National Park (북한산국립공원내 휴식년 계곡의 수질관리를 위한 계류수질모니터링)

  • Park, Jae-Hyeon;Ma, Ho-Seop
    • Journal of the Korean Society of Environmental Restoration Technology
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    • v.2 no.2
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    • pp.88-96
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    • 1999
  • This research was planned to propose some suggestions on the management of stream water quality in the closed valley areas of the Puk'ansan National Park during July 1998 to June 1999. A closed valley area should designate whole valley area. Stream water quality monitoring should include investigation on cations ($Ca^{2+}$, $Mg^{2+}$, $K^+$, $Na^+$), anions ($Cl^-$, $SO{_4}^{2-}$) and suspended solids. A counterplan for stream water preservation and its practical application should be considered before closing a valley area. Also, the results of stream water quality in the closed valley areas in the National Park should be informed to the public. Discharged water from private areas such as a Buddhist temple, shelter, resting place, shopping center, etc. in the National Park should be checked and cleaned. We need to establish regulations on the utilization of stream side area in the park, and trails near the closed valley should also be included in the areas.

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On a Question of Closed Maps of S. Lin

  • Chen, Huaipeng
    • Kyungpook Mathematical Journal
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    • v.50 no.4
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    • pp.537-543
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    • 2010
  • Let X be a regular $T_1$-space such that each single point set is a $G_{\delta}$ set. Denot 'hereditarily closure-preserving' by 'HCP'. To consider a question of closed maps of S. Lin in [6], we improve some results of Foged in [1], and prove the following propositions. Proposition 1. $D\;=\;\{x{\in}X\;:\;\mid\{F{\in}\cal{F}:x{\in}F\}\mid{\geq}{\aleph}_0\}$ is discrete and closed if $\cal{F}$ is a collection of HCP. Proposition 2. $\cal{H}\;=\;\{{\cup}\cal{F}'\;:\;F'$ is an fininte subcolletion of $\cal{F}_n\}$ is HCP if $\cal{F}$ is a collection of HCP. Proposition 3. Let (X,$\tau$) have a $\sigma$-HCP k-network. Then (X,$\tau$) has a $\sigma$-HCP k-network F = ${\cup}_n\cal{F}_n$ such that such tat: (i) $\cal{F}_n\;\subset\;\cal{F}_{n+1}$, (ii) $D_n\;=\;\{x{\in}X\;:\;\mid\{F{\in}\cal{F}_n\;:\;x{\in}F\}\mid\;{\geq}\;{\aleph}_0\}$ is a discrete closed set and (iii) each $\cal{F}_n$ is closed to finite intersections.

Comparison Study of Open Reduction and Closed Reduction in Treatment of Mandibular Subcondylar Fractures (하악골 과두하부골절 정복술에서 관혈적 정복술과 비관혈적 정복술의 비교 연구)

  • Jang, Ju Yun;Kang, Dong Hee
    • Archives of Craniofacial Surgery
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    • v.9 no.2
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    • pp.51-54
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    • 2008
  • Purpose: The choice of open versus closed reduction for mandibular subcondylar fracture is a debatable issue. To evaluate the advantage of open approach to closed method with IMF(intermaxillary fixation), we conducted a retrospective study to compare the outcomes of each method. Methods: From 2002 to 2006, 29 patients with mandibular subcondylar fractures were treated by open or closed reduction. 17 patients were treated by open reduction and 12 patients by closed reduction and IMF. Each group was assessed for duration of mandibular immobilization, incidences of buccal palsy, malocclusion, TMJ(temporomandibular joint) pain, and deviation of the mandible on mouth opening. Results: All cases showed accurate reduction in anatomical position, no significant displacement and no deviation on mouth opening during the follow-up period. IMF period is statistically shorter in open reduction (p<0.05). Differences in incidence of other complications were not significant statistically. Conclusion: As there are significant independent morbidities associated with IMF which requires postoperative rehabilitation, prolonged temporomandibular immobilization should not be overlooked. Some patients with poor compliances will not tolerate IMF in nonsurgical treatment. In the aspect of patient's convenience and early recovery by short IMF period, open reduction would be recommended as a better treatment method.