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THE LATTICE DISTRIBUTIONS INDUCED BY THE SUM OF I.I.D. UNIFORM (0, 1) RANDOM VARIABLES

  • PARK, C.J.;CHUNG, H.Y.
    • Journal of the Korean Mathematical Society
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    • v.15 no.1
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    • pp.59-61
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    • 1978
  • Let $X_1$, $X_2$, ${\cdots}$, $X_n$ be i.i.d. uniform (0,1) random variables. Let $f_n(x)$ denote the probability density function (p.d.f.) of $T_n={\sum}^n_{i=1}X_i$. Consider a set S(x ; ${\delta}$) of lattice points defined by S(x ; ${\delta}$) = $x{\mid}x={\delta}+j$, j=0, 1, ${\cdots}$, n-1, $0{\leq}{\delta}{\leq}1$} The lattice distribution induced by the p.d.f. of $T_n$ is defined as follow: (1) $f_n^{(\delta)}(x)=\{f_n(x)\;if\;x{\in}S(x;{\delta})\\0\;otherwise.$. In this paper we show that $f_n{^{(\delta)}}(x)$ is a probability function thus we obtain a family of lattice distributions {$f_n{^{(\delta)}}(x)$ : $0{\leq}{\delta}{\leq}1$}, that the mean and variance of the lattice distributions are independent of ${\delta}$.

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Effect of N-3, N-6 Fatty Acid and d-Limonene Treatment on Membrane Lipid Composition and Protein Kinase C Activity in Experimental Rat Hepatocarcinogenesis (쥐의 간 발암과정에서 N-3, N-6 지방산 섭취 및 d-Limonene 투여가 생체막 지질조성 및 Protein Kinase C 활성도에 미치는 영향)

  • 김미정;김정희
    • Journal of the Korean Society of Food Science and Nutrition
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    • v.32 no.8
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    • pp.1328-1336
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    • 2003
  • This study was done to investigate the effects of n-3, n-6 fatty acid and d-limonene on the hepatic membrane lipid composition, protein kinase C (PKC) and glutathione S-transferase (GST) activities in experimental rat hepatocarcinogenesis. Sprague-Dawley female rats were fed with two different types of dietary oil for 20 weeks. Corn oil (CO) and sardine oil (SO) were used at 15% by weight as a source of n-6 and n-3 fatty acid, respectively. One week after feeding, rats were intraperitoneally injected twice with a dose of diethylnitrosamine (DEN, 50 mg/kg body weight) and after 1 week 0.05% phenobarbital (PB) was provided with drinking water. Membrane fractional lipid composition showed that the content of cholesterol was higher in 50 group than CO group and also significantly decreased by d-limonene. The content of phospholipid was increased by carcinogen treatment but not affected by dietary oils or d-limonene. Membrane C/PL molar ratio was significantly decreased by d-limonene or carcinogen treatment in 50 groups but not in CO groups. Fatty acid composition was changed by dietary oils but not by carcinogen treatment or d-limonene. Cytosolic PKC activity was not significantly different by dietary oils, d-limonene or carcinogen treatment. However, membrane PKC activity was significantly increased by carcinogen treatment and decreased by d-limonene. Cytosolic GST activity was affected by d-limonene or carcinogen treatment in all dietary groups. These data indicate that dietary oils, d-limonene and carcinogen treatment can not change much membrane phospholipid composition. But membrane C/PL molar ratio was changed by carcinogen treatment and d -limonene although the effect was different between dietary oils. Therefore, it is suggested that different dietary oils and d-limonene can somewhat modulate the changes of membrane fluidity and activities of membrane bound enzymes like membrane associated PKC during carcinogenesis.

A NOTE ON SKEW DERIVATIONS IN PRIME RINGS

  • De Filippis, Vincenzo;Fosner, Ajda
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.4
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    • pp.885-898
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    • 2012
  • Let m, n, r be nonzero fixed positive integers, R a 2-torsion free prime ring, Q its right Martindale quotient ring, and L a non-central Lie ideal of R. Let D : $R{\rightarrow}R$ be a skew derivation of R and $E(x)=D(x^{m+n+r})-D(x^m)x^{n+r}-x^mD(x^n)x^r-x^{m+n}D(x^r)$. We prove that if $E(x)=0$ for all $x{\in}L$, then D is a usual derivation of R or R satisfies $s_4(x_1,{\ldots},x_4)$, the standard identity of degree 4.

KRONECKER FUNCTION RINGS AND PRÜFER-LIKE DOMAINS

  • Chang, Gyu Whan
    • Korean Journal of Mathematics
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    • v.20 no.4
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    • pp.371-379
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    • 2012
  • Let D be an integral domain, $\bar{D}$ be the integral closure of D, * be a star operation of finite character on D, $*_w$ be the so-called $*_w$-operation on D induced by *, X be an indeterminate over D, $N_*=\{f{\in}D[X]{\mid}c(f)^*=D\}$, and $Kr(D,*)=\{0\}{\cup}\{\frac{f}{g}{\mid}0{\neq}f,\;g{\in}D[X]$ and there is an $0{\neq}h{\in}D[X]$ such that $(c(f)c(h))^*{\subseteq}(c(g)c(h))^*$}. In this paper, we show that D is a *-quasi-Pr$\ddot{u}$fer domain if and only if $\bar{D}[X]_{N_*}=Kr(D,*_w)$. As a corollary, we recover Fontana-Jara-Santos's result that D is a Pr$\ddot{u}$fer *-multiplication domain if and only if $D[X]_{N_*} = Kr(D,*_w)$.

A Field Survey on Concentration of Odor Compounds in Pig Buildings and Boundary Areas (돈사 내 및 부지경계에서 악취물질 발생 조사 연구)

  • Yoo Yong-Hee;Kim Tae-Il;Jeong Jong-Won;Gwak Jeong-Hun;Choi Hee-Chul;Song Jun-Ik;Yang Chang Bum;Jang Young-Kee;Kim Ho-Jung;Song Ki-Pong
    • Journal of Animal Environmental Science
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    • v.11 no.1
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    • pp.45-54
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    • 2005
  • A field survey was conducted to determine the concentration of odor compounds from pig buildings and that were 20 meters within the boundary area. The odor compounds were measured from large, medium and small farms with enclosed and open housing systems and slurry and sawdust manure fermentation treatment methods. Among the odor compounds investigated, ammonia ($NH_3$) had the highest concentration at 0.9 ${\~}$ 21.0 ppm followed by Hydrogen Sulfide($H_2S$) with a wide variation concentration of 51.9 ${\~}$ 6,712.4 pub, Uethylmercaptan($CH_3SH$) with non-detectable (N. D.) ${\~}$ 12.9 ppb, Dimethylsulphide($(CH_3)_2S$), with N. D. ${\~}$ 5.2 ppb and Dimethyldisulphide($(CH_3)_2S_2$) with N. D. ${\~}$ 2.6 ppb. Considering the prevailing wind direction and air velocity ranging from 0.23 to 0.73 m/s within the boundary area, the odorous matters; $NH_3$, $H_2S$, $CH_3SH$, $(CH_3)_2S_2$ and $(CH_3)_2S$ were 0.2${\~}$4.5 ppm, 0.01 ${\~}$0.06 ppb, N. D. ${\~}$0.009ppb, N. D.${\~}$0.002ppb and N. D. for $(CH_3)_2S$ respectively. These findings suggested that the Odor compounds $(CH_3)_2S_2$ had the lower detection in the boundary area whilst $(CH_3)_2S$ had no detection level within a 20-meter distance only. However, with these results odor compounds from pig buildings has to be further investigated under more controlled environmental factors.

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The Variation of Serum Thyroglobulin Measured after Thyrogen Administration (Thyrogen 투여 후 측정된 Thyroglobulin 농도변화)

  • Kim, Ji-Na;An, Jae-seok;Won, Woo-Jae
    • The Korean Journal of Nuclear Medicine Technology
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    • v.22 no.1
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    • pp.80-83
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    • 2018
  • Purpose Assessment of Serum Thyroglobulin (sTg) value in total thyroidectomy patients having an ablation dose of radioactive iodine indicates remaining cancer or metastasis. Especially, sTg in patients on withdrawal thyroxine or thyrogen administration for radioiodine ablation is an important indicator to determine the direction of further treatment and prognosis. Current guidelines suggest measurement of sTg is performed at 72 hours after the last injection of thyrogen. and assumes that sTg reaches maximum serum levels at that time. The purpose of this study is to evaluate the variation of sTg measured after thyrogen administration. Materials and Methods We compared with sTg performed at 24hours(D0) and 72hours(D2) after the last injection of thyrogen. We reviewed D0 and D2 from 276 patients were divided them into three groups according to ablation dose of radioactive iodine, 5mCi(A group), 30~80mCi(B group) and 100~200mCi(C group). We used T-test for comparison between D0 and D2. sTg was measured in serum using immunoradiometric assay (Tg-plus RIA; BRAHMS, Berlin, Germany). Results There is no critical variation between D0 and D2 in A group(n=100)(P=0.32), The case of increase(D2>D0) is 45, no change(D2=D0) is 23, decrease(D2D0 is 91, D2=D0 is 28, D2D0 is 19, D2=D0 is 2. The biggest increase is 143.6 ng/mL from 98.4 to 242. Conclusion There was a significant difference in the group over 30mCi. and the case of D2>D0 is 45%, 58.7%, 90.5% for each group. therefore, D2 increased as the dose of radioactive iodine increased. Furthermore, the most sTg values of D0 and D2 are variation under 2.0 ng/mL, so reproducibility as well as sensitivity of sTg will be important at values below 2ng/mL.

The Effects of Mathematical Activities using 4D-Frame on Young Children's Mathematical Ability and Attitude towards Mathematics (포디프레임(4D-Frame)을 활용한 수학활동이 유아의 수학적 능력과 수학적 태도에 미치는 영향)

  • Yang, Hyo-Sook;Park, Young-Suk;Cho, Kwang-Hyun
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.19 no.8
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    • pp.146-159
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    • 2018
  • The purpose of this study was to investigate the effects of Mathematical Activities using 4D-frame on 5-year-old children's mathematical ability and attitude towards Mathematics. For the study, E, K, and Y preschools located in S city were selected: 28 children from Y preschool as the experimental group(I: n=14, II: n=14) and 28 children from E and K preschool as the comparative group(III: n=14, IV: n=14). During the 8 weeks, the experimental group performed Mathematical Activities using 4D-frame and in the comparison group, Nuri-Curriculum's mathematical activities and mathematics-science integration programs were conducted. The analysis of covariance(ANCOVA) was conducted with the pre-test scores of the experimental group(I, II) and the comparison group(III, IV) as covariance. The results showed that there were statistically significant differences between the experimental and comparative groups. Mathematical Activities for Young Children using 4D-frame enhanced 5-year-old children's mathematical ability and attitude towards Mathematics. The results of this study provide an understanding of the efficiency of early childhood mathematical activities using the 4D-frame in early childhood education and provide basic data for the improvement of mathematical ability and attitude of young children and the applicable educational methods at the field.

Fertilizer Concentration after Flowering Affects Growth and Fruit Setting of Ornamental Pepper (개화 후 비료의 농도가 Ornamental Pepper의 생장과 착과에 미치는 영향)

  • 진영욱;정순주;이범선;강종구
    • Journal of Bio-Environment Control
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    • v.12 no.2
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    • pp.95-100
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    • 2003
  • To evaluate the effect of the fertilizer concentration after flowering on growth a31d fruit setting of ornamental pepper (Capsicum annuum L.), plants were fertilized with $100\;mg{\cdot}L^{-1} of N ($EC=0.8\;dS{\cdot}m^{-1}) until flowering, and then with 0 (no fertilizer), 100, 200 or $300\;mg{\cdot}L^{-1} of N (fertilizer solution EC of 0.15, 0.8, 1.45 or $2.10\;dS{\cdot}m^{-1}, respectively) until harvest. Maximum leaf area and shoot dry mass at the end of the growing period were obtained when plants were fertilized with $200\;mg{\cdot}L^{-1} of N. Total fruit number per plant at the end of the growing period was not different when plants were fertilized with 100,200 or 300 mg{\cdot}L^{-1}of N concentration. When plants were fertilized with $200\;mg{\cdot}L^{-1} of N, the number of fruits per plant was decreased significantly as compared to 100, 200 or $300\;mg{\cdot}L^{-1} of N, whereas the percentage of red fruits at the end of the growing period was maximized. Total fruit fresh weight per plant at the end of the growing period was highest with the concentration of $200\;mg{\cdot}L^{-1} of N. The EC of the growing medium remained within 0.8 to $1.2\;dS{\cdot}m^{-1}\;2.0\;to\;3.0dS{\cdot}m^{-1}, or 3.0 to 4.5 dS{\cdot}m^{-1}when fertilizer concentrations were 100, 200 or $300\;mg{\cdot}L^{-1} of N, respectively. Throughout most of the experiment, the pH of the growing medium remained within 5.4 to 6.2, but dropped to 4.9 near the end of the experiment when fertilizer concentration was 200 or 300\;mg{\cdot}L^{-1} of N. Content of most of the nutrients In the leaf was not affected by the different fertilizer concentration. Only aluminum was significantly affected and decreased linearly with increasing fertilizer concentration. The results from this study indicated that optimal fertilizer concentration after flowering for commercial production of ornamental pepper was 100 or $200\;mg{\cdot}L^{-1} of N. At these concentrations, the EC of the growing medium remained approximately within 0.8 to 1.2 and 2 to $3\;dS{\cdot}m^{-1}, respectively. This appears to be the optimal range for vegetative growth or fruit setting of ornamental pepper plants, and indicates that ornamental pepper can be grown with a fairly wide range of fertilizer concentrations.

Cerebrosides and Terpene Glycosides from the Root of Aster scaber

  • Kwon, Hak-Cheol;Cho, Ock-Ryun;Lee, Kang-Choon;Lee, Kang-Ro
    • Archives of Pharmacal Research
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    • v.26 no.2
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    • pp.132-137
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    • 2003
  • Three cerebrosides 2, 3, and 5 and two terpene glycosides 1 and 4 have been isolated from the methanol extract of the root of Aster scaber. Their structures were determined as 3-Ο-$\beta$-D-glucuronopyranosyl-oleanolic acid methyl ester (1), (2S, 3S, 4R, 2 R, 8Z, 15 Z)-N-2 -hydroxy-15 -tetracosenoyl-1-Ο-$\beta$-D-glucopyranosyl-4-hydroxy-8-sphingenine (2), (2S, 3S, 4R, 8Z)-N-octadecanoyl-1-Ο-$\beta$-D-glucopyranosyl-4-hydroxy-8-sphingenine (3), 1$\alpha$-hydroxy-6$\beta$-Ο-$\beta$-D-glucosyl-eudesm-3-ene (4), and (2S, 3S, 4R, 2 R, 8Z)-N-2 -hydroxy-hexadecanoyl-1-Ο-$\beta$-D-glucopyranosyl-4-hydroxy-8-sphingenine (5) on the basis of spectroscopic methods.