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A GENERAL ITERATIVE ALGORITHM FOR A FINITE FAMILY OF NONEXPANSIVE MAPPINGS IN A HILBERT SPACE

  • Thianwan, Sornsak
    • Journal of applied mathematics & informatics
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    • v.28 no.1_2
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    • pp.13-30
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    • 2010
  • Let C be a nonempty closed convex subset of a real Hilbert space H. Consider the following iterative algorithm given by $x_0\;{\in}\;C$ arbitrarily chosen, $x_{n+1}\;=\;{\alpha}_n{\gamma}f(W_nx_n)+{\beta}_nx_n+((1-{\beta}_n)I-{\alpha}_nA)W_nP_C(I-s_nB)x_n$, ${\forall}_n\;{\geq}\;0$, where $\gamma$ > 0, B : C $\rightarrow$ H is a $\beta$-inverse-strongly monotone mapping, f is a contraction of H into itself with a coefficient $\alpha$ (0 < $\alpha$ < 1), $P_C$ is a projection of H onto C, A is a strongly positive linear bounded operator on H and $W_n$ is the W-mapping generated by a finite family of nonexpansive mappings $T_1$, $T_2$, ${\ldots}$, $T_N$ and {$\lambda_{n,1}$}, {$\lambda_{n,2}$}, ${\ldots}$, {$\lambda_{n,N}$}. Nonexpansivity of each $T_i$ ensures the nonexpansivity of $W_n$. We prove that the sequence {$x_n$} generated by the above iterative algorithm converges strongly to a common fixed point $q\;{\in}\;F$ := $\bigcap^N_{i=1}F(T_i)\;\bigcap\;VI(C,\;B)$ which solves the variational inequality $\langle({\gamma}f\;-\;A)q,\;p\;-\;q{\rangle}\;{\leq}\;0$ for all $p\;{\in}\;F$. Using this result, we consider the problem of finding a common fixed point of a finite family of nonexpansive mappings and a strictly pseudocontractive mapping and the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the several recent results in this area.

AN ERDŐS-KO-RADO THEOREM FOR MINIMAL COVERS

  • Ku, Cheng Yeaw;Wong, Kok Bin
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.3
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    • pp.875-894
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    • 2017
  • Let $[n]=\{1,2,{\ldots},n\}$. A set ${\mathbf{A}}=\{A_1,A_2,{\ldots},A_l\}$ is a minimal cover of [n] if ${\cup}_{1{\leq}i{\leq}l}A_i=[n]$ and $$\bigcup_{{1{\leq}i{\leq}l,}\\{i{\neq}j_0}}A_i{\neq}[n]\text{ for all }j_0{\in}[l]$$. Let ${\mathcal{C}}(n)$ denote the collection of all minimal covers of [n], and write $C_n={\mid}{\mathcal{C}}(n){\mid}$. Let ${\mathbf{A}}{\in}{\mathcal{C}}(n)$. An element $u{\in}[n]$ is critical in ${\mathbf{A}}$ if it appears exactly once in ${\mathbf{A}}$. Two minimal covers ${\mathbf{A}},{\mathbf{B}}{\in}{\mathcal{C}}(n)$ are said to be restricted t-intersecting if they share at least t sets each containing an element which is critical in both ${\mathbf{A}}$ and ${\mathbf{B}}$. A family ${\mathcal{A}}{\subseteq}{\mathcal{C}}(n)$ is said to be restricted t-intersecting if every pair of distinct elements in ${\mathcal{A}}$ are restricted t-intersecting. In this paper, we prove that there exists a constant $n_0=n_0(t)$ depending on t, such that for all $n{\geq}n_0$, if ${\mathcal{A}}{\subseteq}{\mathcal{C}}(n)$ is restricted t-intersecting, then ${\mid}{\mathcal{A}}{\mid}{\leq}{\mathcal{C}}_{n-t}$. Moreover, the bound is attained if and only if ${\mathcal{A}}$ is isomorphic to the family ${\mathcal{D}}_0(t)$ consisting of all minimal covers which contain the singleton parts $\{1\},{\ldots},\{t\}$. A similar result also holds for restricted r-cross intersecting families of minimal covers.

Feature Comparison by Prescription Configuration Analysis among Liuhejian's and Lidongyuan's Books and Hejijufang (방제구성을 이용한 유하간(劉河間) 및 이동원(李東垣)의 저작과 『화제국방(和劑局方)』의 특성 비교)

  • Wu, Yueh-Hwan;Kim, Ki-Wook;Lee, Byung-Wook;Kim, Eun-Ha
    • Journal of Korean Medical classics
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    • v.28 no.1
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    • pp.55-69
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    • 2015
  • Objectives : I hope this prescription configuration analysis among Liuhejian's and Lidongyuan's books and "Hejijufang" would explain the differences among Liuhejian's and Lidongyuan's theories against Hejijufang. Methods : I have searched for frequently used herbs combinations in the books and compared each features with others. And then I'd like to find out similar prescription by comparing composition ratio of configuring herbs. Conclusions : (1) In the composition ratio of configuring each of herbs Liuhejian's composition ratio of configuring herbs is higher than "Hejijufang" and Lidongyuan's prescriptions. (2) Lidongyuan's tendencies are about 'stimulate qi', 'removal of fever', 'removal of damp' and 'supplement of yin'. Liuhejian's tendencies are about 'removal of fever' and 'removal of wind'. Tendencies of "Hejijufan" are about 'heat up inside' and 'supplement of blood'. As I compared Lidongyuan's prescriptions with Liuhejian's, Lidongyuan's tendencies are about 'raising yang', 'supplement of qi', 'stimulation qi' and 'promotion of digestion'. Liuhejian's tendencies are about 'removal of fever' and 'removal of wind'. (3) I could prove that Liuhejian and Lidongyuan had created new theories against tendency of Hejijufang.

Plasmid Profiling and Curing of Lactobacillus Strains Isolated from the Gastrointestinal Tract of Chicken

  • Chin Sieo Chin;Abdullah Norhani;Siang Tan Wen;Wan Ho Yin
    • Journal of Microbiology
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    • v.43 no.3
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    • pp.251-256
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    • 2005
  • In this study, we assessed the susceptibility of 12 Lactobacillus strains, all of which had been isolated from the gastrointestinal tracts of chicken, to three antibiotics (chloramphenicol, erythromycin and tetracycline) used commonly as selective markers in transformation studies of lactic acid bacteria. Among these strains, $17\%,\;58\%,\;and\;25\%$ were found to exhibit a high degree of resistance to $200\;{\mu}g/ml$ of tetracycline, erythromycin, and chloramphenicol, respectively. Seven of the 12 Lactobacillus strains exhibiting resistance to at least $50\;{\mu}g/ml$ of chloramphenicol or erythromycin, and five strains exhibiting resistance to at least $50\;{\mu}g/ml$ of tetracycline, were subsequently subjected to plasmid curing with chemical curing agents, such as novobiocin, acriflavin, SDS, and ethidium bromide. In no cases did the antibiotic resistance of these strains prove to be curable, with the exception of the erythromycin resistance exhibited by five Lactobacillus strains (L. acidophilus I16 and I26, L. fermentum I24 and C17, and L. brevis C10). Analysis of the plasmid profiles of these five cured derivatives revealed that all of the derivatives, except for L. acidophilus I16, possessed profiles similar to those of wild-type strains. The curing of L. acidophilus I16 was accompanied by the loss of 4.4 kb, 6.1 kb, and 11.5 kb plasmids.

A Study of Directorial Ways to Licensed Musical -Focused on Korean Production in 2009- (라이선스 뮤지컬 연출방법 연구 -2009년 <드림걸즈> 한국 프로덕션을 중심으로-)

  • Cho, Joon Hui
    • (The) Research of the performance art and culture
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    • no.25
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    • pp.211-251
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    • 2012
  • I attempted to study the resolution of how I can show the essence of an original musical production to audience, the possibilities of how recreate impossible elements according to Korean musical environment because of cultural and linguistic differences, and verify the meaning of adjusting an original production to Korean one through directorial approaches to licensed musical production. I mainly exemplified 2009 Korean production (Charlotte Theatre, March ~ August, 2009) that I directed. The purpose that I wanted to analyze the case of Korean production mainly is able to prove a wide variety of possible challenges rather than simply licensed ones because the former was recreated in 30 years after the first original production. Recreation and coaching to acting through fine and precise analysis of an original production, Koreanizing Western culture of the licensed musical, resolving the problem of linguistic nuances are the important ways to direct licensed musical. For licensed musical director, cooperation with original creative team and Korean production company must be the most important job.

RINGS WITH A RIGHT DUO FACTOR RING BY AN IDEAL CONTAINED IN THE CENTER

  • Cheon, Jeoung Soo;Kwak, Tai Keun;Lee, Yang;Piao, Zhelin;Yun, Sang Jo
    • Bulletin of the Korean Mathematical Society
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    • v.59 no.3
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    • pp.529-545
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    • 2022
  • This article concerns a ring property that arises from combining one-sided duo factor rings and centers. A ring R is called right CIFD if R/I is right duo by some proper ideal I of R such that I is contained in the center of R. We first see that this property is seated between right duo and right π-duo, and not left-right symmetric. We prove, for a right CIFD ring R, that W(R) coincides with the set of all nilpotent elements of R; that R/P is a right duo domain for every minimal prime ideal P of R; that R/W(R) is strongly right bounded; and that every prime ideal of R is maximal if and only if R/W(R) is strongly regular, where W(R) is the Wedderburn radical of R. It is also proved that a ring R is commutative if and only if D3(R) is right CIFD, where D3(R) is the ring of 3 by 3 upper triangular matrices over R whose diagonals are equal. Furthermore, we show that the right CIFD property does not pass to polynomial rings, and that the polynomial ring over a ring R is right CIFD if and only if R/I is commutative by a proper ideal I of R contained in the center of R.

The Clinical Studies on the Irritable Syndrome by Using D.I.T.I. (과민성대장증후군(過敏性大腸症候群) 환자(患者)에 대한 적외선(赤外線) 체열영상촬영기기(體熱映像撮影器機)( D.I.T.I)의 응용연구)

  • Kim, Dal-Rae;Baik, Tai-Hyun
    • The Journal of Internal Korean Medicine
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    • v.21 no.1
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    • pp.7-12
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    • 2000
  • Objectives : This studies were performed to investigate the correlation between the treatment effects and the changes of the thermal differences at the pre and post-treatment by using the digital infrared computer thermographic imaging (D.I.T.I) to the irritable colon syndrome 30 patients. Methods : The extracts of the gwakhyangjunggisan were administerd to the patients by oral method three times per day during four weeks. we selected the Chung-Wan($CV_{12}$), Chunchu($S_{25}$). Hapkok($LI_4$), Naegwan($P_6$), Yongdo($H_4$) acupoints and treated the patients two times per week during four weeks. One week later, we investigated the changes of the pressure pain around left side Pokkyol($SP_{14}$), the symptoms. and the skin temperature changes on Pokkyol($SP_{14}$) and Kimun($LR_{14}$) around, by using the D.I.T.I. Results : In the correlation between the severity of the pressure pain around left side Pokkyol($SP_{14}$) and the thermal differences on Pokkyol($SP_{14}$) and Kimun($LR_{14}$) around, before the treatment, the more the pain was severe, the more the skin temperature was differential significantly. In the correlation between the severity of the symptoms and the thermal differences on Pokkyol($SP_{14}$) and Kimun($LR_{14}$) around, before the treatment, the more the symptom was severe, the more the skin temperature was differential significantly. In the changes of the pressure pain around left side of Pokkyol($SP_{14}$), the improved were significantly higher than the unimproved. In the changes of the symptoms, the improved were significantly higher than the unimproved. In the correlation between the changes of the pressure pain around left side Pokkyol($SP_{14}$) and the changes of the thermal differences at the pre and post- treatment, the more the pain was improved, the more the thermal change was widened significantly. In the correlation between the changes of the symptoms and the changes of thermal differences at the pre and post-treatment, the more the symptom was improved. the more the thermal change was widened significantly. Conclusions : Above the results, the treatments was effective and the digital infrared computer thermographic imaging (D.I.T.I) was useful to prove the improvements of the pressure pain and the symptom with the irritable bowel syndrome patients.

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Effectiveness of "Picture Book Reading Program for Mothers" for Married Immigrant Women and Their Children (여성결혼이민자와 유아기 자녀를 위한 어머니대상 '그림책 읽기 프로그램'의 효과검증)

  • Hyun, Eun-Ae;Rha, Jong-Hay
    • Korean Journal of Human Ecology
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    • v.21 no.2
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    • pp.165-180
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    • 2012
  • The purpose of the study was to prove the effect of the "Picture Book Reading Program for Mothers" developed to enhance the language competence of married immigrant women and their children. Twenty immigrant mothers with three-year-olds were recruited, and they participated in an 8-week-Picture Book Reading Program developed by the reseacher. The REVT and U-TAP were used to measure linguistic abilities for mothers while PRES was used to measure their children's linguistic abilities. Lee(2004)'s "Effect of dialogic picture book reading teacher training program for toddlers" was used to measure the mother's and children's verbal and non-verbal behaviors. The results of the study were as follows: First, by participating in the PBRPM, the mother's linguistic ability as well as children's vocabulary and receptive language have increased. Second, by participating in the PBRPM in terms of mother-child interaction, mother's verbal behaviors to children (i.e. attention and inquiring) and children's verbal behaviors(i.e. responding and imitation) have increased. In conclusion, "PBRPM" for married immigrant women and their children proved to be effective in enhancing the language competence and verbal interactions between married immigrant women and their children.

Camera Calibration for Machine Vision Based Autonomous Vehicles (머신비젼 기반의 자율주행 차량을 위한 카메라 교정)

  • Lee, Mun-Gyu;An, Taek-Jin
    • Journal of Institute of Control, Robotics and Systems
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    • v.8 no.9
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    • pp.803-811
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    • 2002
  • Machine vision systems are usually used to identify traffic lanes and then determine the steering angle of an autonomous vehicle in real time. The steering angle is calculated using a geometric model of various parameters including the orientation, position, and hardware specification of a camera in the machine vision system. To find the accurate values of the parameters, camera calibration is required. This paper presents a new camera-calibration algorithm using known traffic lane features, line thickness and lane width. The camera parameters considered are divided into two groups: Group I (the camera orientation, the uncertainty image scale factor, and the focal length) and Group II(the camera position). First, six control points are extracted from an image of two traffic lines and then eight nonlinear equations are generated based on the points. The least square method is used to find the estimates for the Group I parameters. Finally, values of the Group II parameters are determined using point correspondences between the image and its corresponding real world. Experimental results prove the feasibility of the proposed algorithm.

Morphometric and Genetic Variability Among Tylenchulus semipenetrans Populations from Citrus Growing Area in Korea

  • Park, Byeong-Yong;Park, Sun-Nam;Lee, Jae-Kook;Bae, Chang-Hwan
    • The Plant Pathology Journal
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    • v.25 no.3
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    • pp.236-240
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    • 2009
  • Tylenchulus semipenetrans, citrus nematode is an important phytopathogenic nematode and responsible for serious damage on citrus. However, little information is available about genetic variability of T. semipenetrans among different populations with variation of conventional diagnostic characteristics. In this study, we compared the morphometric and genetic characteristics among different populations. The mature female of T. semipenetrans collected in this study had thicker cuticle than those in the previous studies. In comparative sequence analysis of T. semipenetrans populations obtained from Jeju in Korea, we observed genetic variations within clones generated from single individuals. To determine whether variability among copies of nuclear ribosomal DNA sequences exists in the genome of T. semipenetrans, PCR-RFLP technique from individuals of Korean isolates with MseI and MspI restriction enzymes was used to prove experimentally that all populations have intra-specific variations. Restriction enzyme digestion created several fragments on 3.0% agarose gel corresponding to several haplotypes in all populations, though some populations displayed fragment deletion. The total length of fragments was larger than before digestion, indicating sequence heterogeneity within the genome of T. semipenetrans.