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GENERALIZED WEYL'S THEOREM FOR ALGEBRAICALLY $k$-QUASI-PARANORMAL OPERATORS

  • Senthilkumar, D.;Naik, P. Maheswari;Sivakumar, N.
    • Journal of the Chungcheong Mathematical Society
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    • v.25 no.4
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    • pp.655-668
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    • 2012
  • An operator $T\;{\varepsilon}\;B(\mathcal{H})$ is said to be $k$-quasi-paranormal operator if $||T^{k+1}x||^2\;{\leq}\;||T^{k+2}x||\;||T^kx||$ for every $x\;{\epsilon}\;\mathcal{H}$, $k$ is a natural number. This class of operators contains the class of paranormal operators and the class of quasi - class A operators. In this paper, using the operator matrix representation of $k$-quasi-paranormal operators which is related to the paranormal operators, we show that every algebraically $k$-quasi-paranormal operator has Bishop's property ($\beta$), which is an extension of the result proved for paranormal operators in [32]. Also we prove that (i) generalized Weyl's theorem holds for $f(T)$ for every $f\;{\epsilon}\;H({\sigma}(T))$; (ii) generalized a - Browder's theorem holds for $f(S)$ for every $S\;{\prec}\;T$ and $f\;{\epsilon}\;H({\sigma}(S))$; (iii) the spectral mapping theorem holds for the B - Weyl spectrum of T.

A Characteristic of Nitrogen and Phosphorus Removal in Anoxic/Oxic Basins combined with Iron Electrolysis (철 전기분해장치와 무산소/호기공정을 결합한 질소, 인제거 특성에 관한 연구)

  • Kim, Young-Gyu
    • Journal of Environmental Health Sciences
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    • v.43 no.6
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    • pp.525-531
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    • 2017
  • Objectives: The purpose of this experiment is to better understand the nitrogen and phosphorus removal ratio according to operating conditions in an iron electrolysis system consisting of an anoxic basin, aerobic basin, and iron precipitation apparatus. Methods: Iron electrolysis consists of an iron precipitation reactor composed of iron plates in oxic and anoxic basins. We studied the interrelation coefficient between T-N and T-P removal rates and F/M ratio, and the C/N ratio and BOD removal rate. Results: The F/M ratio and the T-N and T-P removal rate per unit area have interrelation coefficients of 0.362 and 0.603, respectively. The removal rate per MLVSS and the T-N and T-P removal rate per unit area have respective interrelation coefficients of 0.49 and 0.59. Conclusions: The removal rate of T-N and T-P increased with the increasing F/M ratio in the influent, and they also linearly increased in proportion to the C/N ratio of influent and BOD removal rate of the reactor.

The increased GUS gene inactivation over generation in Arabidopsis transgenic lines (애기장대 형질전환 식물체의 세대경과에 따른 GUS유전자의 비활성화에 관한 연구)

  • Park, Soon-Ki
    • Journal of Life Science
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    • v.12 no.1
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    • pp.67-76
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    • 2002
  • The effect of transgene inactivation in T2, T3 and F2 generations was analyzed in progeny seedlings which had been generated by Agrobacterium (LBA4404/pBI121)-mediated transformation in Arabidopsis thaliana. In a system which investigated in the expression of $\beta$-glucuronidase(GUS)gene in kanamycin-resistant (ke $n^{R}$)seedlings, GUS inactivated seedlings were observed in 5 of 12 tested lines of T2 generation and the frequency of GUS inactivation was approximately 2.3%. Lines with multi-copies of T-DNA exhibited severe GUS gene inactivation with the frequency of 5.8% in T2 generation. In T3 generation lines exhibited GUS gene inactivation with the frequency of 1.3%. In contrast, inactivation increased dramatically up to 12.6% in multi-copy T-DNA line. A similar phenomenon was also found in F2 progeny from a transgenic line which had been crossed with wild-type Arabidopsis plant, WS-O (GUS gene inactivation frequency 9.9%). These results indicate that the foreign gene introduced into the plant was inactivated progressively in its transmission during subsequent generations and the transgenic line with multi-copies of T-DNA tended to show more increased inactivation.

Internet Use Time and Health Risk Behavior in Adolescents (청소년의 인터넷 사용시간과 건강위험행위)

  • Kim, Young-Sook
    • The Journal of Korean Society for School & Community Health Education
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    • v.14 no.2
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    • pp.1-14
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    • 2013
  • Objectives: The purpose of this study was to identify the relationship of internet use time and health risk behaviors among adolescents and provide data to set up a strategy for preventing internet addiction. Methods: The data of the 2011 Youth Health Risk Behavior web-based Survey Collected by Korean Center for Disease Control was analyzed using t-test, ANOVA, Chi-square test for this study. Results: There were significant differences between boys and girls in internet use time. Boy's internet use time was different according to city size(F=13.20, p<.001), grade(F=35.85, p<.001), school record(F=298.95, p<.001), economic state(F=326.75, p<.001), living with parents(t=11.60, p<.001), father's education level(F=147.92, p<.001), and mother's education level(F=110.93, p<.001). Girls' internet use time was also different according to school grade(t=-8.68, p<.001), grade(F=61.03, p<.001), school record(F=233.32, p<.001), economic state(F=185.78, p<.001), living with parents(t=10.81, p<.001), father's education level(F=86.54, p<.001), and mother's education level(F=92.64, p<.001). Regarding the health risk behaviors, present smoking, present alcohol drink, drug use skipping breakfast, eating fast food, drinking soda, sexual behavior, suicidal attempt, engagement time in physical education classes, severe exercise, and sleeping satisfaction made differences in the internet use time. Conclusions: The results suggest that health risk behaviors are influenced by internet use time of adolescents. Thus, these results may be contribute to development of programs to prevent internet addiction.

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Superexchange in the Dense Paramagnet $CuF_{2}$ (밀집된 상자성체 $CuF_{2}$의 초교환 상호작용)

  • Jun Hyeong Kim;Chang Hoon Lee;Cheol Eui Lee
    • Journal of the Korean Magnetics Society
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    • v.5 no.3
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    • pp.171-174
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    • 1995
  • We have studied the paramagnetic $CuF_{2}$ using the techniques of pulsed nuclear magnetic resonance(NMR). The powder sample revealed two well-separated lines from the distinct $^{19}F$ sites at room temperature and at 77 K. The distinct frequency shifts of the two lines appear to arise from electron transfers. Furthermore, the two sites have very short spin-lattice relaxation times ($T_{1}$). The frequency-shifted site has the shorter $T_{1}$ than the unshifted one, reflecting the difference of the electron environments of the two sites.

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A study Health problem and Perceived health status of the rural elderly (농촌노인의 건강문제와 지각된 건강상태에 관한 연구)

  • Park, Jeong-Sook;Oh, Yun-Jung
    • Research in Community and Public Health Nursing
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    • v.14 no.2
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    • pp.274-286
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    • 2003
  • Purpose: The purpose of this study is to provide a basic data that may help develop health promotion programs by identifying health problems and perceived health status of the rural elderly. Method: The subjects of the study were 366 elders recruited from 24 villages located in Mari Myun, Geochang Gun, Korea. The sample was selected using a quota sampling method. The instruments used in the study included 117 items for health problems and 4 items for perceived health status. The data were analyzed with descriptive statistics, Pearson correlation coefficient, t-test, ANOVA and scheffe test using SPSS program. Results: 1) The most prevalent health problem was ailments in 'musculoskeletal system', followed by 'fatigue', 'eyes and ears', 'genitourinary system', 'mood & temper patterns', 'cardiovascular system', 'digestive system', 'nervous system', 'respiratory system' and 'skin'. 2) Womens health problems were more prevalent than men's health problems. 3) The mean score of perceived health status was 7.68. 4) Health problems of the rural elderly were significantly correlated with demographic variables such as education (F=9.532, p=0.000), gender (t=-4.246, p=0.000), marital status (t=-3.531, p=0.000), family type (F=5.742, p=0.00l), and occupation (t=3.356, p=0.001). 5) Perceived health status of the rural elderly was significantly correlated with demographic variables such as education (F=6.408, p=0.002), gender (t=2.949, p=0.003), marital status (t=0.802, p=0.034), family type (F=4.844, p=0.003), and occupation (t=-2.485, p=0.011). 6) Health problems of the rural elderly were significantly correlated with life style pattern variables such as drinking (F=5.223, p=0.006), smoking (F=4.087, p=0.007), salty food intake (F=3.424, p=0.034), greenish yellow vegetables intake (F=6.343, p=0.002) and fat food intake (F=5.327, p=0.005). 7) Perceived health status of the rural elderly was significantly correlated with life style pattern variables such as sleeping hours (F=3.966, p=0.020) and drinking (F=7.231. p=0.001). Conclusion: The findings of this study indicate that nurses need to understand health problems and perceived health status of the rural elderly and to develop health promotion programs for them in the future in the consideration of regional and environmental elements.

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Knowledge and Attitude toward Smoking Behavior in Male Middle School Students (일부 남자 중학생의 흡연에 대한 지식 및 태도)

  • Yang, Soon-Ok;Kim, Shin-Jeong;Choi, Eun-Jin;Baek, Sung-Sook;Yang, Soon-Bun
    • Research in Community and Public Health Nursing
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    • v.13 no.2
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    • pp.387-398
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    • 2002
  • This study was conducted to provide basic data to develop a smoking prevention and non-smoking education program. Data were collected, using a questionnaire, from 438 male middle school students living in Chunchon, Kwangwon- do. The data collection period was from September 2 to 30, 2000. The questionnaire used to measure the subjects' knowledge and attitude toward smoking was based on the guideline for the contents of tobacco smoking surveys for the general population designed by WHO. The collected data were analyzed using the SPSS-Win program. The results were as follows. 1. The subjects' average score for smoking knowledge was 58.52 out of 100 points. 2. The subjects' average score for attitude toward smoking was 63.54 out of 100 points. 3. Smoking knowledge of the subjects was significantly different by their grade (F=9.187, p=.000), father's smoking behavior (t=2.261, p= .024), aware of harmfulness of smoking (F=8.911, p=.000). The subjects' attitude toward smoking was significantly different by mother's smoking behavior (t=-2.557, p=.011), brother's smoking behavior (t=-3.959, p=.000), having a smoking friend or not (t=-4.422, p=.000), subjects' smoking experience (t=-8.304, p=.000), present smoking behavior (t=7.001, p=.000), quantity of smoking (F=3.297, p= .041), abstinence period of smoking (F=3.858, p=.013), thinking about smoking behavior (F=20.999, p=.000), aware of harmfulness of smoking (F=20.964, p=.000), and amount of drinking (F=8.316, p=.000). 4. There was a significant correlation between subjects' knowledge and attitude toward smoking (r=.514, p=.000).

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The consistency estimation in nonlinear regression models with noncompact parameter space

  • Park, Seung-Hoe;Kim, Hae-Kyung;Jang, Sook-Hee
    • Bulletin of the Korean Mathematical Society
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    • v.33 no.3
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    • pp.377-383
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    • 1996
  • We consider in this paper the following nonlinear regression model $$ (1.1) y_t = f(x_t, \theta_o) + \in_t, t = 1, \ldots, n, $$ where $y_t$ is the tth response, $x_t$ is m-vector imput variable, $\theta_o$ is a p-vector of unknown parameter belong to a parameter space $\Theta, f:R^m \times \Theta \ to R^1$ is a nonlinear known function, and $\in_t$ are independent unobservable random errors with finite second moment.

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ON A MOVING GRID NUMBERICAL SCHEME FOR HAMILTON-JACOBI EQUATIONS

  • Hong, Bum-Il
    • Journal of the Korean Mathematical Society
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    • v.33 no.2
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    • pp.249-258
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    • 1996
  • Analysis by the method of characteristics shows that if f and $u_0$ are smooth and $u_0$ has compact support, then the Hamilton-Jacobi equation $$ (H-J) ^{u_t + f(u_x) = 0, x \in R, t > 0, } _{u(x, 0) = u_0(x), x \in R, } $$ has a unique $C^1$ solution u on some maximal time interval $0 \leq t < T$ for which $lim_{t \to T}u(x, t) exists uniformly; but this limiting function is not continuously differentiable.

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