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THE FRACTIONAL WEAK DISCREPANCY OF (M, 2)-FREE POSETS

  • Choi, Jeong-Ok
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.1
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    • pp.1-12
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    • 2019
  • For a finite poset $P=(X,{\preceq})$ the fractional weak discrepancy of P, denoted $wd_F(P)$, is the minimum value t for which there is a function $f:X{\rightarrow}{\mathbb{R}}$ satisfying (1) $f(x)+1{\leq}f(y)$ whenever $x{\prec}y$ and (2) ${\mid}f(x)-f(y){\mid}{\leq}t$ whenever $x{\parallel}y$. In this paper, we determine the range of the fractional weak discrepancy of (M, 2)-free posets for $M{\geq}5$, which is a problem asked in [9]. More precisely, we showed that (1) the range of the fractional weak discrepancy of (M, 2)-free interval orders is $W=\{{\frac{r}{r+1}}:r{\in}{\mathbb{N}}{\cup}\{0\}\}{\cup}\{t{\in}{\mathbb{Q}}:1{\leq}t<M-3\}$ and (2) the range of the fractional weak discrepancy of (M, 2)-free non-interval orders is $\{t{\in}{\mathbb{Q}}:1{\leq}t<M-3\}$. The result is a generalization of a well-known result for semiorders and the main result for split semiorders of [9] since the family of semiorders is the family of (4, 2)-free posets.

BANACH FUNCTION ALGEBRAS OF n-TIMES CONTINUOUSLY DIFFERENTIABLE FUNCTIONS ON Rd VANISHING AT INFINITY AND THEIR BSE-EXTENSIONS

  • Inoue, Jyunji;Takahasi, Sin-Ei
    • Journal of the Korean Mathematical Society
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    • v.56 no.5
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    • pp.1333-1354
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    • 2019
  • In authors' paper in 2007, it was shown that the BSE-extension of $C^1_0(R)$, the algebra of continuously differentiable functions f on the real number space R such that f and df /dx vanish at infinity, is the Lipschitz algebra $Lip_1(R)$. This paper extends this result to the case of $C^n_0(R^d)$ and $C^{n-1,1}_b(R^d)$, where n and d represent arbitrary natural numbers. Here $C^n_0(R^d)$ is the space of all n-times continuously differentiable functions f on $R^d$ whose k-times derivatives are vanishing at infinity for k = 0, ${\cdots}$, n, and $C^{n-1,1}_b(R^d)$ is the space of all (n - 1)-times continuously differentiable functions on $R^d$ whose k-times derivatives are bounded for k = 0, ${\cdots}$, n - 1, and (n - 1)-times derivatives are Lipschitz. As a byproduct of our investigation we obtain an important result that $C^{n-1,1}_b(R^d)$ has a predual.

A Study on Changes of Serum $fT_3\;and\;rT_3$ Concentration in Nonthyroidal Critical Illness (비갑상선 중증 질환에서 혈청 $fT_3$$rT_3$의 변화에 관한 연구)

  • Lee, Jong-Wha;Kim, Ju-Ock;Yu, Cheol-Jae;Moon, Youn-Sung;Shin, Young-Tae;Ro, Heung-Kyu
    • The Korean Journal of Nuclear Medicine
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    • v.19 no.1
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    • pp.103-111
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    • 1985
  • Recently changes in thyroid physiology during acute and chronic medical illness were demonstrated. The serum $fT_3,\;rT_3,\;T_4,\;T_3,\;fT_4$, and TSH concentration were measured by radioimmunoassay method in 49 patients with critical illness and 10 normal subjects to assess the change of thyroid function in critical illness. The results were as follows; 1) The mean serum $fT_3$ concentration was $6.68{\pm}1.05pmol/ml$ in normal subjects while in patients with critical illness the serum $fT_3$ concentration was significantly lowered to $1.55{\pm}1.15pmol/ml$(p<0.001). 2) The mean serum $rT_3$ concentration was $0.22{\pm}0.44ng/ml$ in normal subjects and $0.42{\pm}0.37ng/ml$ in patient with critical illness. There was increment in critically ill patients as compared to normal subjects but no statistically significant difference(p>0.05). 3) The mean serum $T_3$ concentration was $1.24{\pm}0.25ng/ml$ in normal subjects and $0.56{\pm}0.56ng/ml$ in patients with criticial illness and there was significant difference in each other(p<0.005). 4) The mean serum $T_4,\;fT_4$, and TSH concentrations were $7.80{\pm}1.02{\mu}g/dl,\;1.26{\pm}0.39ng/dl,\;1.87{\pm}0.45{\mu}U/ml$ in normal subjects respectively and $6.02{\pm}3.06{\mu}g/dl,\;1.46{\pm}0.80ng/dl,\;1.74{\pm}0.79{\mu}U/ml$ in patients with critical illness and there was no significant difference between critically ill patients and normal subjects. 5) The ratio of mean serum concentration of $fT_3$ and $rT_3(fT_3/rT_3)$, $30.42{\pm}5.58$ in normal subjects was significantly higher(p<0.005) than the coresponding patients with critical illness. 6) The mean serum $fT_3$ concentration in expired cases(n=12) during admission was significant difference between expired and survived cases(p<0.005). The mean serum $rT_3$ centration was $0.67{\pm}0.58ng/ml$ in expired cases and $0.34{\pm}0.22ng/ml$ in survived cases with significant difference(p<0.005). Half of the cases who showed less than $3{\mu}g/dl$ of serum $T_4$ level were expired.

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Effects of CuO and ${B_2}{O_3}$Additions on Microwave Dielectric Properties of $PbWO_4$-$TiO_2$Ceramic (CuO ${B_2}{O_3}$첨가에 따른 $PbWO_4$-$TiO_2$세라믹스의 마이크로파 유전특성)

  • 최병훈;이경호
    • Journal of the Korean Ceramic Society
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    • v.38 no.11
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    • pp.1046-1054
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    • 2001
  • Effects of B$_2$O$_3$and CuO addition on the microwave dielectric properties of the PbWO$_4$-TiO$_2$ceramics were investigated in order to use this material as an LTCC material for fabrication of a multilayered RF passive components module. We found that PbWO$_4$could be used as an LTCC material because of its low sintering temperature (8$50^{\circ}C$) and fairy good microwave dielectric properties($\varepsilon$$_{r}$=21.5, Q$\times$f$_{0}$=37200 GHz and $\tau$$_{f}$ =-31 ppm/$^{\circ}C$). In order to stabilize $\tau$$_{f}$ of PbWO$_4$, TiO$_2$was added to the PbWO$_4$and the mixture was sintered at 8$50^{\circ}C$. A near zero $\tau$$_{f}$ value (+0.2 ppm/$^{\circ}C$) was obtained with 8.7 mol% TiO$_2$addition. $\varepsilon$r and Q$\times$f$_{0}$ values were 22.3 and 21400 GHz, respectively. It was believed that the decrement of Q$\times$f$_{0}$ value with TiO$_2$addition was resulted from increasing grain boundary. In order to improve Q$\times$f$_{0}$, various amounts of B$_2$O$_3$and CuO were added to the 0.913PbWO$_4$-0.087TiO$_2$mixture. The optimum amount of CuO was 0.05 wt%. At this addition, the 0.913PbWO$_4$-0.087TiO$_2$ceramic showed $\varepsilon$$_{r}$=23.5, $\tau$$_{f}$ =-2.2ppm/$^{\circ}C$, and Q$\times$f$_{0}$=32900 GHz after sintered at 8$50^{\circ}C$. In case of B$_2$O$_3$addition, the optimum amount range was 1.0~2.5 wt% at which we could obtain following results; $\varepsilon$$_{r}$=20.3~22.1, Q$\times$f$_{0}$=48700~54700 GHz, and $\tau$$_{f}$ =+2.4~+8.2ppm/$^{\circ}C$.

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Screening of Resistant Lines and Yield Losses to F1 Corn from Feeding by the Aphid and Mite (진딧물과 응애 가해에 의한 옥수수 F1의 수량감소율 과 저항성계통 선발)

  • Lee, Joon-Soo;Kim, Soon-Kwon
    • Korean Journal of Breeding Science
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    • v.42 no.5
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    • pp.555-564
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    • 2010
  • Aphid and mite are the major insects that harm corn. These insects are difficult to control because they are very sensitive to environmental conditions. The purpose of this experiment was to information the loss in quantity of corn and to select inbred lines with resistance after exposing corn to aphid and mite. When exposed to aphid, the average loss in grain yield, ear length, ear diameter, 100 kernel weight, kernel length, kernel width, and kernel thickness were 18.4, 10.9, 1.7, 5.4, 2.3, 1.5 and -0.2%, respectively. When exposed to mite, the average loss in grain yield, ear length, ear diameter, 100 kernel weight, kernel length, kernel width, and kernel thickness were 49.7, 16.5, 20.7, 18.9, 9.5, and -3.4, respectively. Mite had more significant impact on the loss than aphid. Among these factors, grain yield and ear dimater were most significantly correlated on the loss to aphid ($r=0.83^{**}$), while kernel length and thickness were most significantly correlated on the loss to mite ($r=0.83^{**}$). However, ear length was not related to loss to the two insects. The inbred lines that were often used for $F_1$ hybrid which was lower than the average loss by aphid, were KS7, B68, 61B3, 70A1, and KS5, while the inbred lines that were often used for $F_1$ hybrid which was lower than the average decrease by mite, were KS7, B68, 61B3, 66B2-4, 70A1, 72B2, and KS5. These inbred lines could be used to breed inbred lines, hybrid, and open pollination variety that confer resistant to aphid and mite.

Intrageneric Protoplast Fusion between Alkalophilic Bacillus sp. F204 and Bacillus sp. K 17 (호알칼리성 Bacillus sp. F204와 Bacillus sp. K 17의 원형질체 융합)

  • 성낙계;노종수;박석규;정영철
    • Microbiology and Biotechnology Letters
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    • v.16 no.4
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    • pp.275-281
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    • 1988
  • To develop cellulase and xylanase-producing strain by protoplast fusion, alkalophilic Bacillus sp. F204 and K17 were treated with NTG(N-methyl-N'-nitro-N-nitrosoguanidine) and isolated anti-biotics resistant strains of S20 (Km$^r$ , Cm$^r$) and G70 (Str$^r$). The frequency of protoplast formation was about 95% when cells of mid-log phase were treated with 200$\mu\textrm{g}$/ml Iysozyme at 37$^{\circ}C$ for 30-45 minutes. Under addition of 0.4-0.5M sodium succinate, 0.5% casamino acid, 1.5% polyvinylpyrrolidone, 25mM MgC1$_2$ and 50mM CaC1$_2$ to the regeneration medium, the regeneration frequency of Bacillus sp. F204 and K17 was 24.9% and 26.2%, respectively. The fusion frequency was 6.6$\times$10$^{-6}$ in the presence of 30% polyethylene glycol 6000 containing 50mM $Ca^{++}$ at 45$^{\circ}C$ for 5 minutes. Cellulase complex and xylanase activities of fusant were compared with parental strains.

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A Comparison of Dizziness Handicap Inventory Scores with Stability Index and Fourier Harmony Index in Healthy Individuals

  • Sang-Seok Yeo;Heun-Jae Ryu
    • The Journal of Korean Physical Therapy
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    • v.35 no.4
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    • pp.105-110
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    • 2023
  • Purpose: The purpose of this study was to determine whether the degree of dizziness affects static balance due to the disruption or absence of the senses involved in balance. To this end, the correlation between the Dizziness Handicap Inventory (DHI), which objectively evaluates dizziness, the Fourier Index (FI; Frequency bands of postural oscillation, F1, F2-4, F5-6, F7-8) and the Stability Index (ST), which evaluates static balance ability, were examined. Methods: This study investigated balance and dizziness issues in 30 healthy young adults. Participants underwent multiple tests like the DHI and tetra-ataxiometric posturography (Tetrax) under different conditions (eyes open/closed, standing on a foam-rubber pillow, and with the head in various orientations). Results: We found that F1 exhibited a weak positive correlation with dizziness under normal conditions, as well as when the eyes were closed (r=0.396, p<0.05) and the head was tilted back (r=0.375, p<0.05). Meanwhile, F5-6 showed a moderate positive correlation with dizziness in both head-back (HB: r=0.471, p<0.05) and head-forward postures (r=0.404, p<0.05). Lastly, both F7-8 and ST demonstrated a moderate positive correlation with dizziness when the head was in a forward posture (F7-8: r=0.483; ST: r=0.403, p<0.05). Conclusion: The study results indicate that the severity of dizziness affects sensory systems and balance. It also suggests that head movements, especially forward and backward, further stimulate the vestibular system, intensifying dizziness, and balance problems in affected individuals.

Photoluminescence of the Single Crystal MnF2(1.5% EuF3) (단결정 MnF2(1.5% EuF3)의 Photoluminescence)

  • Kwon, Soon-Hyuk;Nahm, Kyun;Kim, Chul-Koo
    • Journal of the Korean Magnetics Society
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    • v.17 no.1
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    • pp.1-5
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    • 2007
  • The 1R(Infra-Red) spectrum and PL(Photoluminescence) of the antiferromagnetic pure $MnF_2$ and the single crystal $MnF_2(1.5%\;EuF_3)$ with the rutile structures were measured. The detailed analysis of the measured PL data showed the differences of the optical property between the single crystal $MnF_2(1.5%\;EuF_3)$ and the pure $MnF_2$. It was found that the additional PL peak by the doping of the $EuF_3$ in $MnF_2$ is originated from the f-d transition of $Eu^{3+}$ from the temperature dependent intensity measurement.

Identification of Phellinus linteus by Morphological Characteristics and Molecular Analysis (형태적.분자생물학적 방법에 의한 Phellinus linteus의 동정에 관한 연구)

  • Kim, Sang-Hee;Kim, Soo-Ho;Sung, Jae-Mo;Harrington, Thomas C.
    • The Korean Journal of Mycology
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    • v.27 no.5 s.92
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    • pp.337-340
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    • 1999
  • The context and upper surface of Phellinus basidiocarp become blackened, rimose and woody. The basidiocarp is sessile, dimidiate and elongate. The basidiospores are pigmented and ovoid to globose. Hymenial setae are $17{\sim}35{\times}6{\sim}8{\mu}m$. Nineteen isolates of Phellinus species, including Phellinus linteus, were used for sequencing of the internal transcribed spacer (ITS) region of the nuclear rDNA. Based on these sequence data, specific primers were designed for identification of Phellinus linteus isolates in Korea. The specific primers were within the ITS1 and ITS2 regions and were nested within the universal primers flanking the spacer regions. A total of four primers (the universal primers ITS-1F and ITS-4, and the specific primers PL-F and PL-R) were used for detection of Phellinus linteus collected in Korea. The length of the four amplification products of Phellinus linteus DNA were 800 bp (ITS-1F/ITS-4), two bands of about 720 bp (ITS-1F/PL-R and PL-F/ITS-4), and 610 bp (PL-F/PL-R). Among 23 isolates of Phellinus species collected in Korea, Thirteen isolates were identified as Phellinus linteus based on the presence of the four bands. The other species produced only the single ITS-1F/ITS-4 product.

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Anti-Obesity Effect of Red Garlic Composites in Rats Fed a High Fat-Cholesterol Diet (고지방-콜레스테롤 식이성 흰쥐에서 홍마늘 복합물의 항비만 효과)

  • Lee, Soo-Jung;Hwang, Cho-Rong;Kang, Jae-Ran;Shin, Jung-Hye;Kang, Min-Jung;Sung, Nak-Ju
    • Journal of Life Science
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    • v.22 no.5
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    • pp.671-680
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    • 2012
  • Three kinds of dietary composites-R+T, R+F, and R+TF-were combined in green tea (T), dietary fiber (F), and green tea dietary fiber mixture (TF) to red garlic extract (RG), respectively. The effects of their diets on anti-obesity were investigated $in$ $vitro$ and $in$ $vitro$ in obese rats induced high fat-cholesterol. In $in$ $vivo$ rats, the total phenolic content of the R+T and R+TF was 1.9~2.0 times higher, and their total cholesterol adsorption was 9.5~11.5 times higher than that of RG. $In$ $vivo$, male Sprague-Dawley rats were divided into 6 groups (Normal, HFC, HRG, HR+T, HR+F and HR+TF). Afterwards, the diets of the HRG, HR+T, HR+F, and HR+TF groups were supplemented with 1% of RG and its dietary composites (R+T, R+F, and R+TF) for 4 weeks, respectively. The final body weight of the HRG, HR+T, HR+F, and HR+TF groups decreased significantly compared to the group fed high fat-cholesterol (HFC), but the food efficiency ratio was not significantly different from the HFC group. The liver weight of the HFC group doubled compared to the normal group, whereas that of HR+T and HR+TF groups decreased significantly. The weight of visceral and epididymal fat decreased significantly in the groups fed the composites compared to the HFC group. The obesity index of HR+TF group decreased significantly only when compared to the HFC group. The serum lipid profile such as total lipids, cholesterol, triglyceride, LDL- and VLDL-cholesterol, as well as the atherogenic index and cardiac risk factors decreased drastically in all experimental groups compared to the HFC group, and the levels of HR+T, HR+F and HR+TF groups were a similar trend. GPT activity was not significantly different among the groups fed the composites, and it decreased significantly in the HRG group. The content of the lipid peroxide level decreased significantly in the HRG group and in the groups fed the composites, compared to the HFC group. Serum antioxidant activity was the highest in the HR+T group. We suggest that the hypolipidemic and anti-obesity effect of the RG composites, achieved by mixing green tea extract and/or dietary fiber, was due to their total phenolic content and total cholesterol adsorption effect.